LMFDB - Embedded newform 552.2.bb.a.13.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(13,552)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 0, 14]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("552.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.bb (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$48$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			13.20
Character	$\chi$	$=$	552.13
Dual form			552.2.bb.a.85.20

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.355714 - 1.36875i) q^{2} +(0.540641 - 0.841254i) q^{3} +(-1.74694 + 0.973765i) q^{4} +(0.190010 + 0.0867748i) q^{5} +(-1.34378 - 0.440755i) q^{6} +(2.41838 + 0.710100i) q^{7} +(1.95425 + 2.04473i) q^{8} +(-0.415415 - 0.909632i) q^{9} +O(q^{10})$	\(q+(-0.355714 - 1.36875i) q^{2} +(0.540641 - 0.841254i) q^{3} +(-1.74694 + 0.973765i) q^{4} +(0.190010 + 0.0867748i) q^{5} +(-1.34378 - 0.440755i) q^{6} +(2.41838 + 0.710100i) q^{7} +(1.95425 + 2.04473i) q^{8} +(-0.415415 - 0.909632i) q^{9} +(0.0511834 - 0.290943i) q^{10} +(4.36540 + 3.78264i) q^{11} +(-0.125281 + 1.99607i) q^{12} +(1.69874 + 5.78537i) q^{13} +(0.111696 - 3.56274i) q^{14} +(0.175727 - 0.112933i) q^{15} +(2.10356 - 3.40221i) q^{16} +(0.569168 + 3.95865i) q^{17} +(-1.09729 + 0.892167i) q^{18} +(-6.83272 - 0.982398i) q^{19} +(-0.416434 + 0.0334354i) q^{20} +(1.90485 - 1.65056i) q^{21} +(3.62464 - 7.32066i) q^{22} +(3.93147 - 2.74655i) q^{23} +(2.77668 - 0.538552i) q^{24} +(-3.24573 - 3.74577i) q^{25} +(7.31444 - 4.38308i) q^{26} +(-0.989821 - 0.142315i) q^{27} +(-4.91622 + 1.11443i) q^{28} +(0.673989 - 0.0969050i) q^{29} +(-0.217085 - 0.200354i) q^{30} +(0.246501 - 0.158417i) q^{31} +(-5.40503 - 1.66903i) q^{32} +(5.54227 - 1.62736i) q^{33} +(5.21593 - 2.18719i) q^{34} +(0.397898 + 0.344780i) q^{35} +(1.61147 + 1.18455i) q^{36} +(1.94862 - 0.889905i) q^{37} +(1.08584 + 9.70172i) q^{38} +(5.78537 + 1.69874i) q^{39} +(0.193896 + 0.558099i) q^{40} +(4.71909 - 10.3334i) q^{41} +(-2.93678 - 2.02013i) q^{42} +(-3.10617 + 4.83330i) q^{43} +(-11.3095 - 2.35715i) q^{44} -0.208887i q^{45} +(-5.15781 - 4.40420i) q^{46} +3.14610 q^{47} +(-1.72485 - 3.60900i) q^{48} +(-0.544467 - 0.349908i) q^{49} +(-3.97246 + 5.77501i) q^{50} +(3.63794 + 1.66139i) q^{51} +(-8.60117 - 8.45250i) q^{52} +(0.724646 - 2.46792i) q^{53} +(0.157300 + 1.40544i) q^{54} +(0.501233 + 1.09755i) q^{55} +(3.27414 + 6.33264i) q^{56} +(-4.52050 + 5.21693i) q^{57} +(-0.372386 - 0.888050i) q^{58} +(2.17725 + 7.41504i) q^{59} +(-0.197013 + 0.368403i) q^{60} +(-6.75974 - 10.5184i) q^{61} +(-0.304516 - 0.281046i) q^{62} +(-0.358701 - 2.49482i) q^{63} +(-0.361841 + 7.99181i) q^{64} +(-0.179247 + 1.24669i) q^{65} +(-4.19890 - 7.00709i) q^{66} +(-2.83098 + 2.45306i) q^{67} +(-4.84909 - 6.36127i) q^{68} +(-0.185034 - 4.79226i) q^{69} +(0.330379 - 0.667264i) q^{70} +(7.73672 + 8.92865i) q^{71} +(1.04813 - 2.62706i) q^{72} +(1.62593 - 11.3086i) q^{73} +(-1.91121 - 2.35062i) q^{74} +(-4.90592 + 0.705364i) q^{75} +(12.8930 - 4.93728i) q^{76} +(7.87113 + 12.2477i) q^{77} +(0.267205 - 8.52297i) q^{78} +(-2.27930 + 0.669262i) q^{79} +(0.694924 - 0.463918i) q^{80} +(-0.654861 + 0.755750i) q^{81} +(-15.8224 - 2.78351i) q^{82} +(-13.0165 + 5.94443i) q^{83} +(-1.72039 + 4.73829i) q^{84} +(-0.235363 + 0.801573i) q^{85} +(7.72047 + 2.53229i) q^{86} +(0.282864 - 0.619387i) q^{87} +(0.796589 + 16.3183i) q^{88} +(-14.0921 - 9.05642i) q^{89} +(-0.285913 + 0.0743040i) q^{90} +15.1975i q^{91} +(-4.19353 + 8.62637i) q^{92} -0.293016i q^{93} +(-1.11911 - 4.30621i) q^{94} +(-1.21304 - 0.779574i) q^{95} +(-4.32626 + 3.64465i) q^{96} +(-2.56200 + 5.60999i) q^{97} +(-0.285260 + 0.869704i) q^{98} +(1.62736 - 5.54227i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9}+O(q^{10}) $ 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9	$ 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32} + 6 q^{34} - 22 q^{36} + 90 q^{38} - 74 q^{40} + 90 q^{42} - 130 q^{44} + 96 q^{46} - 88 q^{48} - 48 q^{49} + 142 q^{50} - 142 q^{52} + 18 q^{54} - 82 q^{56} + 22 q^{58} + 2 q^{60} - 40 q^{62} - 8 q^{63} + 16 q^{66} - 44 q^{68} + 16 q^{71} - 4 q^{72} + 10 q^{74} - 138 q^{76} - 40 q^{79} - 170 q^{80} - 48 q^{81} - 124 q^{82} - 8 q^{84} - 216 q^{86} - 108 q^{88} + 4 q^{90} - 198 q^{92} - 238 q^{94} + 80 q^{95} + 4 q^{96} - 132 q^{98}+O(q^{100}) $ 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9 - 4 * q^10 - 4 * q^14 - 8 * q^15 - 8 * q^16 - 4 * q^18 + 20 * q^20 + 20 * q^22 - 8 * q^23 - 4 * q^24 + 48 * q^25 + 16 * q^30 + 16 * q^31 + 4 * q^32 + 6 * q^34 - 22 * q^36 + 90 * q^38 - 74 * q^40 + 90 * q^42 - 130 * q^44 + 96 * q^46 - 88 * q^48 - 48 * q^49 + 142 * q^50 - 142 * q^52 + 18 * q^54 - 82 * q^56 + 22 * q^58 + 2 * q^60 - 40 * q^62 - 8 * q^63 + 16 * q^66 - 44 * q^68 + 16 * q^71 - 4 * q^72 + 10 * q^74 - 138 * q^76 - 40 * q^79 - 170 * q^80 - 48 * q^81 - 124 * q^82 - 8 * q^84 - 216 * q^86 - 108 * q^88 + 4 * q^90 - 198 * q^92 - 238 * q^94 + 80 * q^95 + 4 * q^96 - 132 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{7}{11}\right)$	$1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.355714	−	1.36875i	−0.251528	−	0.967850i
$2$	−0.355714	−	1.36875i	−0.251528	−	0.967850i
$3$	0.540641	−	0.841254i	0.312139	−	0.485698i
$3$	0.540641	−	0.841254i	0.312139	−	0.485698i
$4$	−1.74694	+	0.973765i	−0.873468	+	0.486882i
$5$	0.190010	+	0.0867748i	0.0849752	+	0.0388069i	0.457449	−	0.889236i	$-0.348763\pi$
$5$	0.190010	+	0.0867748i	0.0849752	+	0.0388069i	−0.372474	+	0.928043i	$0.621490\pi$
$6$	−1.34378	−	0.440755i	−0.548594	−	0.179937i
$7$	2.41838	+	0.710100i	0.914061	+	0.268392i	0.704749	−	0.709457i	$-0.251060\pi$
$7$	2.41838	+	0.710100i	0.914061	+	0.268392i	0.209312	+	0.977849i	$0.432878\pi$
$8$	1.95425	+	2.04473i	0.690930	+	0.722921i
$9$	−0.415415	−	0.909632i	−0.138472	−	0.303211i
$10$	0.0511834	−	0.290943i	0.0161856	−	0.0920042i
$11$	4.36540	+	3.78264i	1.31622	+	1.14051i	0.980060	+	0.198703i	$0.0636728\pi$
$11$	4.36540	+	3.78264i	1.31622	+	1.14051i	0.336157	+	0.941806i	$0.390873\pi$
$12$	−0.125281	+	1.99607i	−0.0361656	+	0.576216i
$13$	1.69874	+	5.78537i	0.471145	+	1.60457i	0.761845	+	0.647759i	$0.224294\pi$
$13$	1.69874	+	5.78537i	0.471145	+	1.60457i	−0.290700	+	0.956814i	$0.593888\pi$
$14$	0.111696	−	3.56274i	0.0298520	−	0.952182i
$15$	0.175727	−	0.112933i	0.0453725	−	0.0291591i
$16$	2.10356	−	3.40221i	0.525891	−	0.850552i
$17$	0.569168	+	3.95865i	0.138043	+	0.960114i	0.934638	+	0.355600i	$0.115723\pi$
$17$	0.569168	+	3.95865i	0.138043	+	0.960114i	−0.796595	+	0.604514i	$0.793367\pi$
$18$	−1.09729	+	0.892167i	−0.258633	+	0.210286i
$19$	−6.83272	−	0.982398i	−1.56753	−	0.225377i	−0.696849	−	0.717218i	$-0.745415\pi$
$19$	−6.83272	−	0.982398i	−1.56753	−	0.225377i	−0.870685	+	0.491840i	$0.836324\pi$
$20$	−0.416434	+	0.0334354i	−0.0931174	+	0.00747638i
$21$	1.90485	−	1.65056i	0.415672	−	0.360182i
$22$	3.62464	−	7.32066i	0.772776	−	1.56077i
$23$	3.93147	−	2.74655i	0.819768	−	0.572696i
$23$	3.93147	−	2.74655i	0.819768	−	0.572696i
$24$	2.77668	−	0.538552i	0.566788	−	0.109932i
$25$	−3.24573	−	3.74577i	−0.649146	−	0.749154i
$26$	7.31444	−	4.38308i	1.43448	−	0.859593i
$27$	−0.989821	−	0.142315i	−0.190491	−	0.0273885i
$28$	−4.91622	+	1.11443i	−0.929078	+	0.210608i
$29$	0.673989	−	0.0969050i	0.125157	−	0.0179948i	−0.0794518	−	0.996839i	$-0.525317\pi$
$29$	0.673989	−	0.0969050i	0.125157	−	0.0179948i	0.204608	+	0.978844i	$0.434408\pi$
$30$	−0.217085	−	0.200354i	−0.0396341	−	0.0365794i
$31$	0.246501	−	0.158417i	0.0442729	−	0.0284525i	−0.518317	−	0.855188i	$-0.673441\pi$
$31$	0.246501	−	0.158417i	0.0442729	−	0.0284525i	0.562590	+	0.826736i	$0.309805\pi$
$32$	−5.40503	−	1.66903i	−0.955483	−	0.295046i
$33$	5.54227	−	1.62736i	0.964786	−	0.283287i
$34$	5.21593	−	2.18719i	0.894524	−	0.375101i
$35$	0.397898	+	0.344780i	0.0672570	+	0.0582785i
$36$	1.61147	+	1.18455i	0.268578	+	0.197425i
$37$	1.94862	−	0.889905i	0.320351	−	0.146300i	−0.248748	−	0.968568i	$-0.580019\pi$
$37$	1.94862	−	0.889905i	0.320351	−	0.146300i	0.569100	+	0.822269i	$0.307292\pi$
$38$	1.08584	+	9.70172i	0.176147	+	1.57383i
$39$	5.78537	+	1.69874i	0.926401	+	0.272016i
$40$	0.193896	+	0.558099i	0.0306576	+	0.0882432i
$41$	4.71909	−	10.3334i	0.736997	−	1.61380i	−0.0514343	−	0.998676i	$-0.516379\pi$
$41$	4.71909	−	10.3334i	0.736997	−	1.61380i	0.788432	−	0.615123i	$-0.210893\pi$
$42$	−2.93678	−	2.02013i	−0.453155	−	0.311712i
$43$	−3.10617	+	4.83330i	−0.473687	+	0.737071i	−0.993077	−	0.117466i	$-0.962523\pi$
$43$	−3.10617	+	4.83330i	−0.473687	+	0.737071i	0.519390	+	0.854537i	$0.326159\pi$
$44$	−11.3095	−	2.35715i	−1.70497	−	0.355354i
$45$		−	0.208887i		−	0.0311390i
$46$	−5.15781	−	4.40420i	−0.760478	−	0.649364i
$47$	3.14610			0.458905			0.229453	−	0.973320i	$-0.426306\pi$
$47$	3.14610			0.458905			0.229453	+	0.973320i	$0.426306\pi$
$48$	−1.72485	−	3.60900i	−0.248960	−	0.520915i
$49$	−0.544467	−	0.349908i	−0.0777810	−	0.0499868i
$50$	−3.97246	+	5.77501i	−0.561791	+	0.816709i
$51$	3.63794	+	1.66139i	0.509414	+	0.232642i
$52$	−8.60117	−	8.45250i	−1.19277	−	1.17215i
$53$	0.724646	−	2.46792i	0.0995378	−	0.338995i	−0.894634	−	0.446799i	$-0.852564\pi$
$53$	0.724646	−	2.46792i	0.0995378	−	0.338995i	0.994172	+	0.107804i	$0.0343820\pi$
$54$	0.157300	+	1.40544i	0.0214059	+	0.191256i
$55$	0.501233	+	1.09755i	0.0675862	+	0.147993i
$56$	3.27414	+	6.33264i	0.437526	+	0.846234i
$57$	−4.52050	+	5.21693i	−0.598754	+	0.690999i
$58$	−0.372386	−	0.888050i	−0.0488967	−	0.116607i
$59$	2.17725	+	7.41504i	0.283454	+	0.965356i	0.970973	+	0.239189i	$0.0768817\pi$
$59$	2.17725	+	7.41504i	0.283454	+	0.965356i	−0.687519	+	0.726167i	$0.741300\pi$
$60$	−0.197013	+	0.368403i	−0.0254343	+	0.0475606i
$61$	−6.75974	−	10.5184i	−0.865496	−	1.34674i	−0.937012	−	0.349298i	$-0.886420\pi$
$61$	−6.75974	−	10.5184i	−0.865496	−	1.34674i	0.0715158	−	0.997439i	$-0.477216\pi$
$62$	−0.304516	−	0.281046i	−0.0386736	−	0.0356929i
$63$	−0.358701	−	2.49482i	−0.0451921	−	0.314318i
$64$	−0.361841	+	7.99181i	−0.0452302	+	0.998977i
$65$	−0.179247	+	1.24669i	−0.0222328	+	0.154632i
$66$	−4.19890	−	7.00709i	−0.516849	−	0.862513i
$67$	−2.83098	+	2.45306i	−0.345859	+	0.299689i	−0.810416	−	0.585854i	$-0.800759\pi$
$67$	−2.83098	+	2.45306i	−0.345859	+	0.299689i	0.464557	+	0.885543i	$0.346214\pi$
$68$	−4.84909	−	6.36127i	−0.588039	−	0.771417i
$69$	−0.185034	−	4.79226i	−0.0222754	−	0.576920i
$70$	0.330379	−	0.667264i	0.0394879	−	0.0797533i
$71$	7.73672	+	8.92865i	0.918180	+	1.05964i	0.998024	+	0.0628285i	$0.0200121\pi$
$71$	7.73672	+	8.92865i	0.918180	+	1.05964i	−0.0798447	+	0.996807i	$0.525442\pi$
$72$	1.04813	−	2.62706i	0.123523	−	0.309602i
$73$	1.62593	−	11.3086i	0.190300	−	1.32357i	−0.640912	−	0.767614i	$-0.721444\pi$
$73$	1.62593	−	11.3086i	0.190300	−	1.32357i	0.831213	−	0.555954i	$-0.187647\pi$
$74$	−1.91121	−	2.35062i	−0.222173	−	0.273254i
$75$	−4.90592	+	0.705364i	−0.566487	+	0.0814485i
$76$	12.8930	−	4.93728i	1.47892	−	0.566345i
$77$	7.87113	+	12.2477i	0.896999	+	1.39576i
$78$	0.267205	−	8.52297i	0.0302550	−	0.965036i
$79$	−2.27930	+	0.669262i	−0.256441	+	0.0752978i	−0.407426	−	0.913238i	$-0.633574\pi$
$79$	−2.27930	+	0.669262i	−0.256441	+	0.0752978i	0.150985	+	0.988536i	$0.451755\pi$
$80$	0.694924	−	0.463918i	0.0776949	−	0.0518676i
$81$	−0.654861	+	0.755750i	−0.0727623	+	0.0839722i
$82$	−15.8224	−	2.78351i	−1.74729	−	0.307388i
$83$	−13.0165	+	5.94443i	−1.42874	+	0.652486i	−0.971540	−	0.236876i	$-0.923876\pi$
$83$	−13.0165	+	5.94443i	−1.42874	+	0.652486i	−0.457204	+	0.889362i	$0.651149\pi$
$84$	−1.72039	+	4.73829i	−0.187710	+	0.516990i
$85$	−0.235363	+	0.801573i	−0.0255287	+	0.0869428i
$86$	7.72047	+	2.53229i	0.832520	+	0.273064i
$87$	0.282864	−	0.619387i	0.0303263	−	0.0664052i
$88$	0.796589	+	16.3183i	0.0849166	+	1.73953i
$89$	−14.0921	−	9.05642i	−1.49376	−	0.959979i	−0.995681	−	0.0928449i	$-0.970404\pi$
$89$	−14.0921	−	9.05642i	−1.49376	−	0.959979i	−0.498075	−	0.867134i	$-0.665960\pi$
$90$	−0.285913	+	0.0743040i	−0.0301379	+	0.00783233i
$91$			15.1975i			1.59313i
$92$	−4.19353	+	8.62637i	−0.437205	+	0.899362i
$93$		−	0.293016i		−	0.0303844i
$94$	−1.11911	−	4.30621i	−0.115427	−	0.444152i
$95$	−1.21304	−	0.779574i	−0.124455	−	0.0799826i
$96$	−4.32626	+	3.64465i	−0.441547	+	0.371981i
$97$	−2.56200	+	5.60999i	−0.260131	+	0.569608i	−0.993962	−	0.109724i	$-0.965003\pi$
$97$	−2.56200	+	5.60999i	−0.260131	+	0.569608i	0.733831	+	0.679332i	$0.237731\pi$
$98$	−0.285260	+	0.869704i	−0.0288156	+	0.0878534i
$99$	1.62736	−	5.54227i	0.163556	−	0.557019i
$100$	9.31758	+	3.38304i	0.931758	+	0.338304i
$101$	11.3221	−	5.17063i	1.12659	−	0.514497i	0.237117	−	0.971481i	$-0.423798\pi$
$101$	11.3221	−	5.17063i	1.12659	−	0.514497i	0.889475	+	0.456984i	$0.151070\pi$
$102$	0.979959	−	5.57040i	0.0970304	−	0.551552i
$103$	7.58841	−	8.75749i	0.747708	−	0.862901i	−0.246636	−	0.969108i	$-0.579325\pi$
$103$	7.58841	−	8.75749i	0.747708	−	0.862901i	0.994344	+	0.106207i	$0.0338706\pi$
$104$	−8.50977	+	14.7795i	−0.834451	+	1.44925i
$105$	0.505167	−	0.148331i	0.0492993	−	0.0144756i
$106$	−3.63572	−	0.113984i	−0.353133	−	0.0110711i
$107$	−2.68053	−	4.17098i	−0.259137	−	0.403224i	0.687169	−	0.726497i	$-0.258853\pi$
$107$	−2.68053	−	4.17098i	−0.259137	−	0.403224i	−0.946306	+	0.323273i	$0.895217\pi$
$108$	1.86774	−	0.715238i	0.179723	−	0.0688238i
$109$	9.47882	−	1.36285i	0.907906	−	0.130537i	0.327488	−	0.944855i	$-0.393798\pi$
$109$	9.47882	−	1.36285i	0.907906	−	0.130537i	0.580419	+	0.814318i	$0.302889\pi$
$110$	1.32397	−	1.07647i	0.126235	−	0.102638i
$111$	0.304868	−	2.12040i	0.0289368	−	0.201260i
$112$	7.50312	−	6.73408i	0.708978	−	0.636311i
$113$	6.04769	+	6.97941i	0.568919	+	0.656567i	0.965185	−	0.261568i	$-0.0842397\pi$
$113$	6.04769	+	6.97941i	0.568919	+	0.656567i	−0.396266	+	0.918136i	$0.629694\pi$
$114$	8.74866	+	4.33168i	0.819387	+	0.405699i
$115$	0.985351	−	0.180721i	0.0918844	−	0.0168523i
$116$	−1.08305	+	0.825594i	−0.100559	+	0.0766545i
$117$	4.55688	−	3.94856i	0.421283	−	0.365044i
$118$	9.37483	−	5.61774i	0.863023	−	0.517155i
$119$	−1.43457	+	9.97767i	−0.131507	+	0.914652i
$120$	0.574331	+	0.138615i	0.0524290	+	0.0126538i
$121$	3.18288	+	22.1374i	0.289353	+	2.01249i
$122$	−11.9924	+	12.9939i	−1.08574	+	1.17641i
$123$	−6.14164	−	9.55658i	−0.553773	−	0.861688i
$124$	−0.276361	+	0.516778i	−0.0248179	+	0.0464080i
$125$	−0.585935	−	1.99551i	−0.0524076	−	0.178484i
$126$	−3.28718	+	1.37841i	−0.292845	+	0.122799i
$127$	5.68698	−	6.56313i	0.504638	−	0.582383i	−0.445080	−	0.895491i	$-0.646825\pi$
$127$	5.68698	−	6.56313i	0.504638	−	0.582383i	0.949718	+	0.313108i	$0.101370\pi$
$128$	11.0675	−	2.34753i	0.978236	−	0.207494i
$129$	2.38671	+	5.22616i	0.210138	+	0.460138i
$130$	1.77016	−	0.198121i	0.155253	−	0.0173764i
$131$	1.76611	−	6.01481i	0.154306	−	0.525517i	−0.845661	−	0.533721i	$-0.820793\pi$
$131$	1.76611	−	6.01481i	0.154306	−	0.525517i	0.999966	+	0.00820412i	$0.00261148\pi$
$132$	−8.09732	+	8.23976i	−0.704782	+	0.717179i
$133$	−15.8265	−	7.22772i	−1.37233	−	0.626723i
$134$	4.36464	+	3.00231i	0.377047	+	0.259360i
$135$	−0.175727	−	0.112933i	−0.0151242	−	0.00971971i
$136$	−6.98207	+	8.89997i	−0.598708	+	0.763166i
$137$	−0.313042			−0.0267450			−0.0133725	−	0.999911i	$-0.504257\pi$
$137$	−0.313042			−0.0267450			−0.0133725	+	0.999911i	$0.504257\pi$
$138$	−6.49357	+	1.95794i	−0.552770	+	0.166671i
$139$		−	5.60105i		−	0.475075i	−0.971378	−	0.237538i	$-0.923660\pi$
$139$		−	5.60105i		−	0.475075i	0.971378	−	0.237538i	$-0.0763403\pi$
$140$	−1.03084	−	0.214850i	−0.0871216	−	0.0181581i
$141$	1.70091	−	2.64667i	0.143242	−	0.222889i
$142$	9.46900	−	13.7657i	0.794621	−	1.15519i
$143$	−14.4683	+	31.6812i	−1.20990	+	2.64931i
$144$	−3.96861	−	0.500142i	−0.330717	−	0.0416785i
$145$	0.136474	+	0.0400723i	0.0113335	+	0.00332782i
$146$	−16.0569	+	1.79713i	−1.32888	+	0.148732i
$147$	−0.588722	+	0.268860i	−0.0485570	+	0.0221752i
$148$	−2.53756	+	3.45211i	−0.208586	+	0.283761i
$149$	1.66760	+	1.44498i	0.136615	+	0.118377i	0.720488	−	0.693468i	$-0.243918\pi$
$149$	1.66760	+	1.44498i	0.136615	+	0.118377i	−0.583873	+	0.811845i	$0.698463\pi$
$150$	2.71057	+	6.46405i	0.221317	+	0.527788i
$151$	−23.0454	+	6.76675i	−1.87541	+	0.550670i	−0.878007	+	0.478647i	$0.841127\pi$
$151$	−23.0454	+	6.76675i	−1.87541	+	0.550670i	−0.997403	+	0.0720229i	$0.977055\pi$
$152$	−11.3441	−	15.8909i	−0.920127	−	1.28892i
$153$	3.36447	−	2.16222i	0.272002	−	0.174805i
$154$	13.9642	−	15.1303i	1.12526	−	1.21923i
$155$	0.0605843	−	0.00871070i	0.00486625	−	0.000699661i
$156$	−11.7608	+	2.66600i	−0.941621	+	0.213451i
$157$	18.5052	+	2.66065i	1.47688	+	0.212343i	0.833208	−	0.552960i	$-0.186502\pi$
$157$	18.5052	+	2.66065i	1.47688	+	0.212343i	0.643671	+	0.765303i	$0.277411\pi$
$158$	1.72683	+	2.88171i	0.137379	+	0.229257i
$159$	−1.68437	−	1.94387i	−0.133579	−	0.154159i
$160$	−0.882180	−	0.786154i	−0.0697425	−	0.0621509i
$161$	11.4581	−	3.85046i	0.903025	−	0.303459i
$162$	1.26737	+	0.627508i	0.0995742	+	0.0493017i
$163$	1.36908	−	1.18632i	0.107235	−	0.0929194i	−0.599593	−	0.800305i	$-0.704671\pi$
$163$	1.36908	−	1.18632i	0.107235	−	0.0929194i	0.706828	+	0.707386i	$0.250125\pi$
$164$	1.81832	+	22.6470i	0.141987	+	1.76843i
$165$	1.19430	+	0.171715i	0.0929763	+	0.0133680i
$166$	12.7666	+	15.7017i	0.990877	+	1.21869i
$167$	−0.591885	−	4.11665i	−0.0458014	−	0.318556i	−0.999823	−	0.0188177i	$-0.994010\pi$
$167$	−0.591885	−	4.11665i	−0.0458014	−	0.318556i	0.954022	−	0.299738i	$-0.0968993\pi$
$168$	7.09749	+	0.669298i	0.547583	+	0.0516375i
$169$	−19.6485	+	12.6273i	−1.51142	+	0.971333i
$170$	1.18087	+	0.0370217i	0.0905688	+	0.00283944i
$171$	1.94480	+	6.62337i	0.148722	+	0.506502i
$172$	0.719786	−	11.4681i	0.0548832	−	0.874438i
$173$	−13.3481	−	11.5662i	−1.01483	−	0.879359i	−0.0221086	−	0.999756i	$-0.507038\pi$
$173$	−13.3481	−	11.5662i	−1.01483	−	0.879359i	−0.992726	+	0.120397i	$0.961583\pi$
$174$	−0.948402	−	0.166845i	−0.0718982	−	0.0126485i
$175$	−5.18953	−	11.3635i	−0.392291	−	0.858998i
$176$	22.0522	−	6.89497i	1.66225	−	0.519728i
$177$	7.41504	+	2.17725i	0.557348	+	0.163652i
$178$	−7.38320	+	22.5100i	−0.553394	+	1.68719i
$179$	9.69685	+	4.42840i	0.724777	+	0.330994i	0.743414	−	0.668832i	$-0.233205\pi$
$179$	9.69685	+	4.42840i	0.724777	+	0.330994i	−0.0186370	+	0.999826i	$0.505933\pi$
$180$	0.203407	+	0.364912i	0.0151610	+	0.0271989i
$181$	−7.44916	+	11.5911i	−0.553692	+	0.861561i	−0.999435	−	0.0335996i	$-0.989303\pi$
$181$	−7.44916	+	11.5911i	−0.553692	+	0.861561i	0.445744	+	0.895161i	$0.352939\pi$
$182$	20.8015	−	5.40596i	1.54191	−	0.400716i
$183$	−12.5032			−0.924263
$184$	13.2990	+	2.67135i	0.980417	+	0.196935i
$185$	0.447479			0.0328993
$186$	−0.401065	+	0.104230i	−0.0294075	+	0.00764252i
$187$	−12.4895	+	19.4340i	−0.913323	+	1.42116i
$188$	−5.49603	+	3.06356i	−0.400839	+	0.223433i
$189$	−2.29270	−	1.04704i	−0.166770	−	0.0761612i
$190$	−0.635543	+	1.93765i	−0.0461072	+	0.140572i
$191$	14.1397	+	4.15180i	1.02311	+	0.300413i	0.749908	−	0.661542i	$-0.230098\pi$
$191$	14.1397	+	4.15180i	1.02311	+	0.300413i	0.273206	+	0.961956i	$0.411916\pi$
$192$	6.52751	+	4.62510i	0.471083	+	0.333788i
$193$	−7.89644	−	17.2908i	−0.568398	−	1.24462i	−0.947646	−	0.319324i	$-0.896544\pi$
$193$	−7.89644	−	17.2908i	−0.568398	−	1.24462i	0.379247	−	0.925295i	$-0.376183\pi$
$194$	8.59000	+	1.51117i	0.616726	+	0.108496i
$195$	0.951872	+	0.824802i	0.0681650	+	0.0590653i
$196$	1.29188	+	0.0810833i	0.0922768	+	0.00579166i
$197$	−5.86293	−	19.9673i	−0.417716	−	1.42261i	−0.852808	−	0.522225i	$-0.825102\pi$
$197$	−5.86293	−	19.9673i	−0.417716	−	1.42261i	0.435091	−	0.900386i	$-0.356716\pi$
$198$	−8.16484	−	0.255977i	−0.580250	−	0.0181915i
$199$	−13.8730	+	8.91566i	−0.983434	+	0.632014i	−0.930387	−	0.366578i	$-0.880529\pi$
$199$	−13.8730	+	8.91566i	−0.983434	+	0.632014i	−0.0530462	+	0.998592i	$0.516893\pi$
$200$	1.31614	−	13.9568i	0.0930649	−	0.986895i
$201$	0.533101	+	3.70780i	0.0376020	+	0.261528i
$202$	−11.1047	−	13.6578i	−0.781325	−	0.960961i
$203$	1.69877	+	0.244247i	0.119230	+	0.0171428i
$204$	−7.97306	+	0.640155i	−0.558226	+	0.0448198i
$205$	1.79335	−	1.55395i	0.125253	−	0.108532i
$206$	−14.6861	−	7.27145i	−1.02323	−	0.506626i
$207$	−4.13154	−	2.43523i	−0.287162	−	0.169260i
$208$	23.2564	+	6.39044i	1.61254	+	0.443097i
$209$	−26.1115	−	30.1343i	−1.80617	−	2.08443i
$210$	−0.382722	−	0.638683i	−0.0264103	−	0.0440733i
$211$	2.81311	+	0.404463i	0.193662	+	0.0278444i	0.238463	−	0.971152i	$-0.423356\pi$
$211$	2.81311	+	0.404463i	0.193662	+	0.0278444i	−0.0448011	+	0.998996i	$0.514265\pi$
$212$	1.13726	+	5.01693i	0.0781075	+	0.344564i
$213$	11.6940	−	1.68135i	0.801263	−	0.115204i
$214$	−4.75552	+	5.15264i	−0.325081	+	0.352227i
$215$	−1.00961	+	0.648839i	−0.0688550	+	0.0442504i
$216$	−1.64336	−	2.30204i	−0.111816	−	0.156634i
$217$	0.708624	−	0.208071i	0.0481045	−	0.0141248i
$218$	−5.23714	−	12.4893i	−0.354704	−	0.845883i
$219$	−8.63433	−	7.48169i	−0.583454	−	0.505566i
$220$	−1.94437	−	1.42926i	−0.131090	−	0.0963607i
$221$	−21.9354	+	10.0176i	−1.47553	+	0.673854i
$222$	−3.01074	+	0.336970i	−0.202068	+	0.0226160i
$223$	8.55889	+	2.51312i	0.573146	+	0.168291i	0.555446	−	0.831553i	$-0.312548\pi$
$223$	8.55889	+	2.51312i	0.573146	+	0.168291i	0.0176997	+	0.999843i	$0.494366\pi$
$224$	−11.8862	−	7.87446i	−0.794181	−	0.526135i
$225$	−2.05895	+	4.50847i	−0.137263	+	0.300565i
$226$	7.40179	−	10.7604i	0.492360	−	0.715773i
$227$	2.26730	−	3.52799i	0.150486	−	0.234161i	−0.757823	−	0.652460i	$-0.773737\pi$
$227$	2.26730	−	3.52799i	0.150486	−	0.234161i	0.908309	+	0.418299i	$0.137374\pi$
$228$	2.81695	−	13.5155i	0.186557	−	0.895088i
$229$			3.13780i			0.207351i	0.994611	+	0.103676i	$0.0330604\pi$
$229$			3.13780i			0.207351i	−0.994611	+	0.103676i	$0.966940\pi$
$230$	−0.597864	−	1.28441i	−0.0394220	−	0.0846915i
$231$	14.5589			0.957905
$232$	1.51529	+	1.18875i	0.0994834	+	0.0780453i
$233$	−5.10382	−	3.28003i	−0.334362	−	0.214882i	0.362676	−	0.931915i	$-0.381863\pi$
$233$	−5.10382	−	3.28003i	−0.334362	−	0.214882i	−0.697039	+	0.717034i	$0.745499\pi$
$234$	−7.02552	−	4.83265i	−0.459272	−	0.315920i
$235$	0.597791	+	0.273002i	0.0389956	+	0.0178087i
$236$	−11.0240	−	10.8335i	−0.717603	−	0.705198i
$237$	−0.669262	+	2.27930i	−0.0434732	+	0.148056i
$238$	14.1672	−	1.58563i	0.918324	−	0.102781i
$239$	0.205268	+	0.449474i	0.0132777	+	0.0290740i	0.916155	−	0.400825i	$-0.131276\pi$
$239$	0.205268	+	0.449474i	0.0132777	+	0.0290740i	−0.902877	+	0.429899i	$0.858549\pi$
$240$	−0.0145680	−	0.835421i	−0.000940361	−	0.0539262i
$241$	10.9064	−	12.5866i	0.702541	−	0.810776i	−0.286552	−	0.958065i	$-0.592509\pi$
$241$	10.9064	−	12.5866i	0.702541	−	0.810776i	0.989094	+	0.147289i	$0.0470546\pi$
$242$	29.1683	−	12.2311i	1.87501	−	0.786248i
$243$	0.281733	+	0.959493i	0.0180732	+	0.0615515i
$244$	22.0512	+	11.7925i	1.41169	+	0.754937i
$245$	−0.0730911	−	0.113732i	−0.00466962	−	0.00726607i
$246$	−10.8959	+	11.8058i	−0.694695	+	0.752708i
$247$	−5.92348	−	41.1987i	−0.376902	−	2.62141i
$248$	0.805643	+	0.194443i	0.0511584	+	0.0123471i
$249$	−2.03647	+	14.1640i	−0.129056	+	0.897604i
$250$	−2.52292	+	1.51183i	−0.159564	+	0.0956163i
$251$	16.8344	−	14.5871i	1.06258	−	0.920727i	0.0655535	−	0.997849i	$-0.479119\pi$
$251$	16.8344	−	14.5871i	1.06258	−	0.920727i	0.997022	+	0.0771224i	$0.0245732\pi$
$252$	3.05599	+	4.00900i	0.192510	+	0.252543i
$253$	27.5516	+	2.88154i	1.73216	+	0.181161i
$254$	−11.0062	−	5.44944i	−0.690590	−	0.341928i
$255$	0.547079	+	0.631363i	0.0342594	+	0.0395375i
$256$	−7.15003	−	14.3135i	−0.446877	−	0.894595i
$257$	2.35328	−	16.3674i	0.146794	−	1.02097i	−0.774630	−	0.632414i	$-0.782064\pi$
$257$	2.35328	−	16.3674i	0.146794	−	1.02097i	0.921424	−	0.388559i	$-0.127027\pi$
$258$	6.30430	−	5.12581i	0.392489	−	0.319119i
$259$	5.34442	−	0.768412i	0.332086	−	0.0477468i
$260$	−0.900848	−	2.35243i	−0.0558682	−	0.145891i
$261$	−0.368133	−	0.572827i	−0.0227869	−	0.0354571i
$262$	−8.86099	−	0.277802i	−0.547434	−	0.0171627i
$263$	7.83744	−	2.30128i	0.483277	−	0.141903i	−0.0310135	−	0.999519i	$-0.509873\pi$
$263$	7.83744	−	2.30128i	0.483277	−	0.141903i	0.514291	+	0.857616i	$0.328055\pi$
$264$	14.1585	+	8.15219i	0.871394	+	0.501733i
$265$	0.351843	−	0.406049i	0.0216136	−	0.0249434i
$266$	−4.26321	+	24.2335i	−0.261394	+	1.48585i
$267$	−15.2375	+	6.95873i	−0.932519	+	0.425867i
$268$	2.55684	−	7.04204i	0.156184	−	0.430161i
$269$	4.28400	−	14.5900i	0.261200	−	0.889566i	−0.719573	−	0.694416i	$-0.755663\pi$
$269$	4.28400	−	14.5900i	0.261200	−	0.889566i	0.980773	−	0.195150i	$-0.0625192\pi$
$270$	−0.0920679	+	0.280697i	−0.00560307	+	0.0170827i
$271$	−7.62800	+	16.7030i	−0.463368	+	1.01463i	0.523339	+	0.852125i	$0.324686\pi$
$271$	−7.62800	+	16.7030i	−0.463368	+	1.01463i	−0.986707	+	0.162510i	$0.948041\pi$
$272$	14.6654	+	6.39085i	0.889222	+	0.387502i
$273$	12.7849	+	8.21638i	0.773780	+	0.497278i
$274$	0.111353	+	0.428475i	0.00672710	+	0.0258851i
$275$		−	28.6292i		−	1.72641i
$276$	4.98978	+	8.19159i	0.300349	+	0.493076i
$277$			16.6080i			0.997878i	0.866637	+	0.498939i	$0.166277\pi$
$277$			16.6080i			0.997878i	−0.866637	+	0.498939i	$0.833723\pi$
$278$	−7.66643	+	1.99237i	−0.459802	+	0.119495i
$279$	−0.246501	−	0.158417i	−0.0147576	−	0.00948415i
$280$	0.0726075	+	1.48738i	0.00433913	+	0.0888879i
$281$	−5.99935	+	13.1367i	−0.357891	+	0.783672i	0.641966	+	0.766733i	$0.278119\pi$
$281$	−5.99935	+	13.1367i	−0.357891	+	0.783672i	−0.999857	+	0.0169385i	$0.994608\pi$
$282$	−4.22765	−	1.38666i	−0.251753	−	0.0825742i
$283$	−1.63467	+	5.56718i	−0.0971711	+	0.330935i	−0.993703	−	0.112044i	$-0.964260\pi$
$283$	−1.63467	+	5.56718i	−0.0971711	+	0.330935i	0.896532	+	0.442979i	$0.146078\pi$
$284$	−22.2100	−	8.06403i	−1.31792	−	0.478512i
$285$	−1.31164	+	0.599005i	−0.0776947	+	0.0354820i
$286$	48.5101	+	8.53401i	2.86846	+	0.504626i
$287$	18.7502	−	21.6389i	1.10679	−	1.27731i
$288$	0.727123	+	5.60993i	0.0428461	+	0.330568i
$289$	0.964427	−	0.283181i	0.0567310	−	0.0166577i
$290$	0.00630322	−	0.201052i	0.000370138	−	0.0118062i
$291$	3.33430	+	5.18828i	0.195460	+	0.304142i
$292$	8.17150	+	21.3386i	0.478201	+	1.24875i
$293$	−4.17079	+	0.599670i	−0.243660	+	0.0350331i	−0.263063	−	0.964779i	$-0.584733\pi$
$293$	−4.17079	+	0.599670i	−0.243660	+	0.0350331i	0.0194025	+	0.999812i	$0.493824\pi$
$294$	0.577418	+	0.710174i	0.0336757	+	0.0414182i
$295$	−0.229738	+	1.59786i	−0.0133759	+	0.0930312i
$296$	5.62770	+	2.24531i	0.327104	+	0.130506i
$297$	−3.78264	−	4.36540i	−0.219491	−	0.253306i
$298$	1.38463	−	2.79652i	0.0802092	−	0.161998i
$299$	22.5684	+	18.0793i	1.30516	+	1.04555i
$300$	7.88346	−	6.00944i	0.455152	−	0.346955i
$301$	−10.9440	+	9.48305i	−0.630803	+	0.546594i
$302$	17.4595	+	29.1363i	1.00468	+	1.67661i
$303$	1.77138	−	12.3202i	0.101763	−	0.707778i
$304$	−17.7154	+	21.1798i	−1.01605	+	1.21475i
$305$	−0.371691	−	2.58517i	−0.0212830	−	0.148026i
$306$	−4.15632	−	3.83598i	−0.237601	−	0.219288i
$307$	−15.9820	−	24.8685i	−0.912142	−	1.41932i	−0.907834	−	0.419330i	$-0.862265\pi$
$307$	−15.9820	−	24.8685i	−0.912142	−	1.41932i	−0.00430825	−	0.999991i	$-0.501371\pi$
$308$	−25.6767	−	13.7313i	−1.46307	−	0.782416i
$309$	−3.26467	−	11.1184i	−0.185720	−	0.632505i
$310$	−0.0334734	−	0.0798260i	−0.00190116	−	0.00453381i
$311$	−17.3341	+	20.0047i	−0.982929	+	1.13436i	0.00799972	+	0.999968i	$0.497454\pi$
$311$	−17.3341	+	20.0047i	−0.982929	+	1.13436i	−0.990928	+	0.134392i	$0.957092\pi$
$312$	7.83258	+	15.1493i	0.443432	+	0.857659i
$313$	−1.24374	−	2.72340i	−0.0703002	−	0.153936i	0.871220	−	0.490893i	$-0.163329\pi$
$313$	−1.24374	−	2.72340i	−0.0703002	−	0.153936i	−0.941520	+	0.336957i	$0.890602\pi$
$314$	−2.94081	−	26.2754i	−0.165960	−	1.48281i
$315$	0.148331	−	0.505167i	0.00835748	−	0.0284630i
$316$	3.33008	−	3.38866i	0.187332	−	0.190627i
$317$	−4.70433	−	2.14839i	−0.264221	−	0.120666i	0.278900	−	0.960320i	$-0.410030\pi$
$317$	−4.70433	−	2.14839i	−0.264221	−	0.120666i	−0.543121	+	0.839654i	$0.682758\pi$
$318$	−2.06151	+	2.99694i	−0.115604	+	0.168060i
$319$	3.30879	+	2.12643i	0.185257	+	0.119057i
$320$	−0.762241	+	1.48713i	−0.0426106	+	0.0831329i
$321$	−4.95806			−0.276732
$322$	−9.34612	−	14.3136i	−0.520839	−	0.797664i
$323$		−	27.6075i		−	1.53612i
$324$	0.408077	−	1.95793i	0.0226709	−	0.108774i
$325$	16.1570	−	25.1408i	0.896231	−	1.39456i
$326$	−2.11077	−	1.45194i	−0.116905	−	0.0804153i
$327$	3.97814	−	8.71090i	0.219991	−	0.481714i
$328$	30.3512	−	10.5447i	1.67586	−	0.582232i
$329$	7.60845	+	2.23404i	0.419467	+	0.123167i
$330$	−0.189796	−	1.69578i	−0.0104479	−	0.0933495i
$331$	−18.5154	+	8.45572i	−1.01770	+	0.464768i	−0.853186	−	0.521607i	$-0.825333\pi$
$331$	−18.5154	+	8.45572i	−1.01770	+	0.464768i	−0.164514	+	0.986375i	$0.552606\pi$
$332$	16.9505	−	23.0595i	0.930278	−	1.26556i
$333$	−1.61897	−	1.40285i	−0.0887192	−	0.0768756i
$334$	−5.42411	+	2.27449i	−0.296794	+	0.124455i
$335$	−0.750779	+	0.220449i	−0.0410194	+	0.0120444i
$336$	−1.60858	−	9.95275i	−0.0877551	−	0.542967i
$337$	−17.0822	+	10.9781i	−0.930527	+	0.598013i	−0.915694	−	0.401877i	$-0.868358\pi$
$337$	−17.0822	+	10.9781i	−0.930527	+	0.598013i	−0.0148328	+	0.999890i	$0.504722\pi$
$338$	24.2729	+	22.4021i	1.32027	+	1.21851i
$339$	9.14108	−	1.31429i	0.496475	−	0.0713824i
$340$	−0.369380	−	1.62948i	−0.0200324	−	0.0883712i
$341$	1.67531	+	0.240873i	0.0907230	+	0.0130440i
$342$	8.37392	−	5.01796i	0.452810	−	0.271340i
$343$	−12.6222	−	14.5668i	−0.681533	−	0.786531i
$344$	−15.9530	+	3.09417i	−0.860129	+	0.166827i
$345$	0.380689	−	0.926635i	0.0204956	−	0.0498883i
$346$	−11.0831	+	22.3844i	−0.595829	+	1.20339i
$347$	−6.73110	+	5.83253i	−0.361344	+	0.313107i	−0.816545	−	0.577282i	$-0.804113\pi$
$347$	−6.73110	+	5.83253i	−0.361344	+	0.313107i	0.455200	+	0.890389i	$0.349568\pi$
$348$	0.108991	+	1.35747i	0.00584254	+	0.0727681i
$349$	−12.2865	−	1.76653i	−0.657680	−	0.0945602i	−0.194609	−	0.980881i	$-0.562344\pi$
$349$	−12.2865	−	1.76653i	−0.657680	−	0.0945602i	−0.463072	+	0.886321i	$0.653253\pi$
$350$	−13.7077	+	11.1453i	−0.732710	+	0.595741i
$351$	−0.858103	−	5.96824i	−0.0458022	−	0.318561i
$352$	−17.2817	−	27.7313i	−0.921120	−	1.47808i
$353$	4.05166	−	2.60384i	0.215648	−	0.138589i	−0.428358	−	0.903609i	$-0.640908\pi$
$353$	4.05166	−	2.60384i	0.215648	−	0.138589i	0.644006	+	0.765021i	$0.277271\pi$
$354$	0.342473	−	10.9238i	0.0182022	−	0.580593i
$355$	0.695274	+	2.36789i	0.0369013	+	0.125674i
$356$	33.4367	+	2.09862i	1.77214	+	0.111227i
$357$	7.61817	+	6.60118i	0.403196	+	0.349371i
$358$	2.61206	−	14.8478i	0.138052	−	0.784730i
$359$	−0.655620	−	1.43561i	−0.0346023	−	0.0757685i	0.891542	−	0.452939i	$-0.149624\pi$
$359$	−0.655620	−	1.43561i	−0.0346023	−	0.0757685i	−0.926144	+	0.377170i	$0.876897\pi$
$360$	0.427117	−	0.408217i	0.0225111	−	0.0215149i
$361$	27.4907	+	8.07198i	1.44688	+	0.424841i
$362$	18.5151	+	6.07289i	0.973131	+	0.319184i
$363$	20.3440	+	9.29078i	1.06778	+	0.487640i
$364$	−14.7988	−	26.5490i	−0.775666	−	1.39155i
$365$	1.29024	−	2.00765i	0.0675343	−	0.105085i
$366$	4.44756	+	17.1137i	0.232478	+	0.894548i
$367$	8.96669			0.468057			0.234029	−	0.972230i	$-0.424809\pi$
$367$	8.96669			0.468057			0.234029	+	0.972230i	$0.424809\pi$
$368$	−1.07424	−	19.1532i	−0.0559986	−	0.998431i
$369$	−11.3599			−0.591374
$370$	−0.159175	−	0.612486i	−0.00827509	−	0.0318416i
$371$	3.50494	−	5.45379i	0.181967	−	0.283147i
$372$	0.285329	+	0.511881i	0.0147936	+	0.0265398i
$373$	3.15179	+	1.43937i	0.163193	+	0.0745280i	0.495337	−	0.868701i	$-0.335045\pi$
$373$	3.15179	+	1.43937i	0.163193	+	0.0745280i	−0.332144	+	0.943229i	$0.607772\pi$
$374$	31.0430	+	10.1820i	1.60519	+	0.526499i
$375$	−1.99551	−	0.585935i	−0.103048	−	0.0302575i
$376$	6.14825	+	6.43292i	0.317072	+	0.331752i
$377$	1.70556	+	3.73466i	0.0878410	+	0.192345i
$378$	−0.617590	+	3.51058i	−0.0317654	+	0.180565i
$379$	−5.67753	−	4.91961i	−0.291635	−	0.252703i	0.496738	−	0.867900i	$-0.334531\pi$
$379$	−5.67753	−	4.91961i	−0.291635	−	0.252703i	−0.788373	+	0.615197i	$0.789076\pi$
$380$	2.87822	+	0.180649i	0.147650	+	0.00926709i
$381$	−2.44664	−	8.33249i	−0.125345	−	0.426886i
$382$	0.653061	−	20.8305i	0.0334135	−	1.06578i
$383$	−6.90273	+	4.43612i	−0.352713	+	0.226675i	−0.704984	−	0.709223i	$-0.749046\pi$
$383$	−6.90273	+	4.43612i	−0.352713	+	0.226675i	0.352271	+	0.935898i	$0.385410\pi$
$384$	4.00866	−	10.5797i	0.204566	−	0.539894i
$385$	0.432802	+	3.01021i	0.0220577	+	0.153414i
$386$	−20.8579	+	16.9588i	−1.06164	+	0.863181i
$387$	5.68687	+	0.817649i	0.289080	+	0.0415634i
$388$	−0.987169	−	12.2951i	−0.0501159	−	0.624188i
$389$	−19.8326	+	17.1850i	−1.00555	+	0.871314i	−0.991698	−	0.128590i	$-0.958955\pi$
$389$	−19.8326	+	17.1850i	−1.00555	+	0.871314i	−0.0138524	+	0.999904i	$0.504410\pi$
$390$	0.790350	−	1.59627i	0.0400210	−	0.0808300i
$391$	13.1103	+	14.0001i	0.663017	+	0.708013i
$392$	−0.348556	−	1.79709i	−0.0176047	−	0.0907669i
$393$	−4.10515	−	4.73760i	−0.207078	−	0.238980i
$394$	−25.2447	+	15.1275i	−1.27181	+	0.762113i
$395$	−0.491165	−	0.0706188i	−0.0247132	−	0.00355322i
$396$	2.55398	+	11.2667i	0.128342	+	0.566171i
$397$	−26.6381	+	3.82998i	−1.33693	+	0.192221i	−0.773422	−	0.633891i	$-0.781457\pi$
$397$	−26.6381	+	3.82998i	−1.33693	+	0.192221i	−0.563505	+	0.826112i	$0.690548\pi$
$398$	17.1381	+	15.8173i	0.859056	+	0.792847i
$399$	−14.6368	+	9.40650i	−0.732757	+	0.470914i
$400$	−19.5715	+	3.16317i	−0.978575	+	0.158159i
$401$	8.00460	−	2.35036i	0.399731	−	0.117372i	−0.0756872	−	0.997132i	$-0.524115\pi$
$401$	8.00460	−	2.35036i	0.399731	−	0.117372i	0.475418	+	0.879760i	$0.342297\pi$
$402$	4.88540	−	2.04859i	0.243662	−	0.102175i
$403$	1.33524	+	1.15699i	0.0665130	+	0.0576338i
$404$	−14.7440	+	20.0578i	−0.733542	+	0.997914i
$405$	−0.190010	+	0.0867748i	−0.00944168	+	0.00431187i
$406$	−0.269965	−	2.41207i	−0.0133982	−	0.119709i
$407$	11.8727	+	3.48614i	0.588508	+	0.172801i
$408$	3.71234	+	10.6854i	0.183788	+	0.529005i
$409$	−6.73387	+	14.7451i	−0.332968	+	0.729099i	−0.999871	−	0.0160457i	$-0.994892\pi$
$409$	−6.73387	+	14.7451i	−0.332968	+	0.729099i	0.666903	+	0.745145i	$0.267620\pi$
$410$	−2.76488	−	1.90188i	−0.136548	−	0.0939272i
$411$	−0.169243	+	0.263347i	−0.00834815	+	0.0129900i
$412$	−4.72872	+	22.6881i	−0.232967	+	1.11776i
$413$			19.4784i			0.958471i
$414$	−1.86357	+	6.52128i	−0.0915893	+	0.320504i
$415$	−2.98909			−0.146729
$416$	0.474256	−	34.1053i	0.0232523	−	1.67215i
$417$	−4.71191	−	3.02816i	−0.230743	−	0.148290i
$418$	−31.9580	+	46.4592i	−1.56312	+	2.27240i
$419$	−10.9304	−	4.99177i	−0.533987	−	0.243864i	0.130124	−	0.991498i	$-0.458462\pi$
$419$	−10.9304	−	4.99177i	−0.533987	−	0.243864i	−0.664111	+	0.747634i	$0.731190\pi$
$420$	−0.738056	+	0.751038i	−0.0360134	+	0.0366469i
$421$	−6.74790	+	22.9812i	−0.328872	+	1.12004i	0.614670	+	0.788784i	$0.289289\pi$
$421$	−6.74790	+	22.9812i	−0.328872	+	1.12004i	−0.943542	+	0.331252i	$0.892529\pi$
$422$	−0.447053	−	3.99430i	−0.0217622	−	0.194440i
$423$	−1.30694	−	2.86179i	−0.0635454	−	0.139145i
$424$	6.46237	−	3.34122i	0.313840	−	0.162264i
$425$	12.9808	−	14.9807i	0.629663	−	0.726670i
$426$	−6.46108	−	15.4081i	−0.313040	−	0.746525i
$427$	−8.87852	−	30.2374i	−0.429661	−	1.46329i
$428$	8.74427	+	4.67623i	0.422670	+	0.226034i
$429$	18.8297	+	29.2996i	0.909108	+	1.41460i
$430$	1.24723	+	1.15110i	0.0601467	+	0.0555111i
$431$	−1.39568	−	9.70715i	−0.0672274	−	0.467577i	−0.995429	−	0.0955002i	$-0.969555\pi$
$431$	−1.39568	−	9.70715i	−0.0672274	−	0.467577i	0.928202	−	0.372077i	$-0.121354\pi$
$432$	−2.56634	+	3.06821i	−0.123473	+	0.147619i
$433$	−0.927383	+	6.45009i	−0.0445672	+	0.309972i	0.955329	+	0.295545i	$0.0955013\pi$
$433$	−0.927383	+	6.45009i	−0.0445672	+	0.309972i	−0.999896	+	0.0144264i	$0.995408\pi$
$434$	−0.536864	−	0.895913i	−0.0257703	−	0.0430052i
$435$	0.107494	−	0.0931443i	0.00515396	−	0.00446593i
$436$	−15.2318	+	11.6109i	−0.729470	+	0.556064i
$437$	−29.5609	+	14.9042i	−1.41409	+	0.712963i
$438$	−7.16919	+	14.4796i	−0.342557	+	0.691860i
$439$	−15.6599	−	18.0725i	−0.747405	−	0.862552i	0.246909	−	0.969039i	$-0.420585\pi$
$439$	−15.6599	−	18.0725i	−0.747405	−	0.862552i	−0.994314	+	0.106487i	$0.966040\pi$
$440$	−1.26465	+	3.16976i	−0.0602900	+	0.151112i
$441$	−0.0921074	+	0.640621i	−0.00438607	+	0.0305058i
$442$	21.5142	+	26.4606i	1.02333	+	1.25860i
$443$	−5.03264	+	0.723584i	−0.239108	+	0.0343785i	−0.260827	−	0.965386i	$-0.583995\pi$
$443$	−5.03264	+	0.723584i	−0.239108	+	0.0343785i	0.0217190	+	0.999764i	$0.493086\pi$
$444$	1.53219	+	4.00108i	0.0727145	+	0.189883i
$445$	−1.89177	−	2.94365i	−0.0896784	−	0.139542i
$446$	0.395304	−	12.6089i	0.0187182	−	0.597049i
$447$	2.11717	−	0.621656i	0.100139	−	0.0294033i
$448$	−6.55005	+	19.0703i	−0.309461	+	0.900986i
$449$	5.35031	−	6.17459i	0.252497	−	0.291397i	−0.615324	−	0.788274i	$-0.710975\pi$
$449$	5.35031	−	6.17459i	0.252497	−	0.291397i	0.867821	+	0.496878i	$0.165520\pi$
$450$	6.90335	+	1.21445i	0.325427	+	0.0572499i
$451$	59.6880	−	27.2586i	2.81060	−	1.28356i
$452$	−17.3612	−	6.30354i	−0.816603	−	0.296494i
$453$	−6.76675	+	23.0454i	−0.317930	+	1.08277i
$454$	−5.63543	−	1.84840i	−0.264484	−	0.0867499i
$455$	−1.31876	+	2.88768i	−0.0618243	+	0.135376i
$456$	−19.5014	+	0.951974i	−0.913236	+	0.0445803i
$457$	19.4119	+	12.4753i	0.908051	+	0.583569i	0.909168	−	0.416430i	$-0.136719\pi$
$457$	19.4119	+	12.4753i	0.908051	+	0.583569i	−0.00111654	+	0.999999i	$0.500355\pi$
$458$	4.29485	−	1.11616i	0.200685	−	0.0521546i
$459$		−	3.99936i		−	0.186674i
$460$	−1.54536	+	1.27521i	−0.0720530	+	0.0594568i
$461$		−	18.6881i		−	0.870391i	−0.900336	−	0.435195i	$-0.856679\pi$
$461$		−	18.6881i		−	0.870391i	0.900336	−	0.435195i	$-0.143321\pi$
$462$	−5.17880	−	19.9274i	−0.240940	−	0.927108i
$463$	30.2126	+	19.4164i	1.40410	+	0.902358i	0.999924	−	0.0123242i	$-0.00392302\pi$
$463$	30.2126	+	19.4164i	1.40410	+	0.902358i	0.404173	+	0.914683i	$0.367559\pi$
$464$	1.08809	−	2.49690i	0.0505133	−	0.115916i
$465$	0.0254264	−	0.0556761i	0.00117912	−	0.00258192i
$466$	−2.67402	+	8.15259i	−0.123872	+	0.377661i
$467$	−1.04167	+	3.54761i	−0.0482029	+	0.164164i	−0.980077	−	0.198618i	$-0.936355\pi$
$467$	−1.04167	+	3.54761i	−0.0482029	+	0.164164i	0.931874	+	0.362782i	$0.118173\pi$
$468$	−4.11560	+	11.3352i	−0.190244	+	0.523970i
$469$	−8.58830	+	3.92214i	−0.396571	+	0.181108i
$470$	0.161028	−	0.915335i	0.00742766	−	0.0422212i
$471$	12.2430	−	14.1291i	0.564126	−	0.651036i
$472$	−10.9069	+	18.9427i	−0.502029	+	0.871909i
$473$	−31.8423	+	9.34975i	−1.46411	+	0.429902i
$474$	3.35785	+	0.105272i	0.154231	+	0.00483532i
$475$	18.4973	+	28.7824i	0.848716	+	1.32063i
$476$	−7.20980	−	18.8273i	−0.330461	−	0.862947i
$477$	−2.54593	+	0.366049i	−0.116570	+	0.0167602i
$478$	0.542199	−	0.440844i	0.0247996	−	0.0201637i
$479$	−5.37801	+	37.4049i	−0.245728	+	1.70907i	0.376649	+	0.926356i	$0.377076\pi$
$479$	−5.37801	+	37.4049i	−0.245728	+	1.70907i	−0.622377	+	0.782718i	$0.713833\pi$
$480$	−1.13830	+	0.317111i	−0.0519559	+	0.0144741i
$481$	8.45863	+	9.76178i	0.385680	+	0.445099i
$482$	−21.1075	−	10.4508i	−0.961418	−	0.476022i
$483$	2.95550	−	11.7209i	0.134480	−	0.533319i
$484$	−27.1169	−	35.5733i	−1.23259	−	1.61697i
$485$	−0.973611	+	0.843639i	−0.0442094	+	0.0383077i
$486$	1.21309	−	0.726926i	0.0550267	−	0.0329740i
$487$	−2.92088	+	20.3152i	−0.132358	+	0.920569i	0.810111	+	0.586276i	$0.199407\pi$
$487$	−2.92088	+	20.3152i	−0.132358	+	0.920569i	−0.942469	+	0.334293i	$0.891503\pi$
$488$	8.29701	−	34.3773i	0.375588	−	1.55619i
$489$	−0.257811	−	1.79311i	−0.0116586	−	0.0810875i
$490$	−0.129671	+	0.140499i	−0.00585793	+	0.00634711i
$491$	2.28446	+	3.55468i	0.103096	+	0.160421i	0.888969	−	0.457967i	$-0.151422\pi$
$491$	2.28446	+	3.55468i	0.103096	+	0.160421i	−0.785873	+	0.618388i	$0.787786\pi$
$492$	20.0349	+	10.7142i	0.903243	+	0.483034i
$493$	0.767226	+	2.61293i	0.0345541	+	0.117681i
$494$	−54.2835	+	22.7627i	−2.44233	+	1.02414i
$495$	0.790144	−	0.911875i	0.0355143	−	0.0409857i
$496$	−0.0204353	−	1.17189i	−0.000917571	−	0.0526193i
$497$	12.3701	+	27.0867i	0.554874	+	1.21500i
$498$	20.1113	−	2.25091i	0.901208	−	0.100866i
$499$	4.17031	−	14.2028i	0.186689	−	0.635803i	−0.811954	−	0.583721i	$-0.801596\pi$
$499$	4.17031	−	14.2028i	0.186689	−	0.635803i	0.998643	−	0.0520817i	$-0.0165856\pi$
$500$	2.96675	+	2.91546i	0.132677	+	0.130384i
$501$	−3.78314	−	1.72770i	−0.169018	−	0.0771881i
$502$	−25.9542	−	17.8532i	−1.15839	−	0.796825i
$503$	11.8887	+	7.64042i	0.530092	+	0.340669i	0.778153	−	0.628075i	$-0.216157\pi$
$503$	11.8887	+	7.64042i	0.530092	+	0.340669i	−0.248061	+	0.968744i	$0.579793\pi$
$504$	4.40024	−	5.60894i	0.196002	−	0.249842i
$505$	2.60000			0.115698
$506$	−5.85641	−	38.7362i	−0.260349	−	1.72204i
$507$			23.3562i			1.03729i
$508$	−3.54385	+	17.0031i	−0.157233	+	0.754392i
$509$	−8.86210	+	13.7897i	−0.392806	+	0.611218i	−0.980183	−	0.198096i	$-0.936524\pi$
$509$	−8.86210	+	13.7897i	−0.392806	+	0.611218i	0.587377	+	0.809314i	$0.300161\pi$
$510$	0.669573	−	0.973398i	0.0296492	−	0.0431028i
$511$	11.9623	−	26.1938i	0.529182	−	1.15875i
$512$	−17.0482	+	14.8781i	−0.753432	+	0.657526i
$513$	6.62337	+	1.94480i	0.292429	+	0.0858649i
$514$	−23.2400	+	2.60108i	−1.02507	+	0.114729i
$515$	2.20180	−	1.00553i	0.0970231	−	0.0443090i
$516$	−9.25847	−	6.80567i	−0.407581	−	0.299603i
$517$	13.7340	+	11.9006i	0.604019	+	0.523386i
$518$	−2.95285	−	7.04183i	−0.129741	−	0.309400i
$519$	−16.9466	+	4.97597i	−0.743872	+	0.218421i
$520$	−2.89943	+	2.06982i	−0.127148	+	0.0907677i
$521$	3.96667	−	2.54922i	0.173783	−	0.111683i	−0.450858	−	0.892596i	$-0.648882\pi$
$521$	3.96667	−	2.54922i	0.173783	−	0.111683i	0.624641	+	0.780912i	$0.285245\pi$
$522$	−0.653104	+	0.707644i	−0.0285856	+	0.0309727i
$523$	23.8003	−	3.42197i	1.04071	−	0.149632i	0.399295	−	0.916823i	$-0.369255\pi$
$523$	23.8003	−	3.42197i	1.04071	−	0.149632i	0.641419	+	0.767191i	$0.278346\pi$
$524$	2.77174	+	12.2273i	0.121084	+	0.534151i
$525$	−12.3652	−	1.77785i	−0.539663	−	0.0775919i
$526$	−5.93775	−	9.90887i	−0.258898	−	0.432047i
$527$	0.767416	+	0.885646i	0.0334292	+	0.0385793i
$528$	6.12192	−	22.2792i	0.266422	−	0.969578i
$529$	7.91290	−	21.5960i	0.344039	−	0.938955i
$530$	−0.680933	−	0.337147i	−0.0295779	−	0.0146447i
$531$	5.84049	−	5.06082i	0.253456	−	0.219621i
$532$	34.6860	−	2.78493i	1.50383	−	0.120742i
$533$	67.7988	+	9.74799i	2.93669	+	0.422232i
$534$	14.9449	+	18.3809i	0.646730	+	0.795421i
$535$	−0.147392	−	1.02513i	−0.00637230	−	0.0443203i
$536$	−10.5483	−	0.994710i	−0.455616	−	0.0429649i
$537$	8.96792	−	5.76333i	0.386994	−	0.248706i
$538$	−21.4939	−	0.673857i	−0.926666	−	0.0290520i
$539$	−1.05324	−	3.58701i	−0.0453663	−	0.154503i
$540$	0.416953	+	0.0261697i	0.0179428	+	0.00112616i
$541$	−14.6834	−	12.7232i	−0.631288	−	0.547014i	0.279366	−	0.960185i	$-0.409876\pi$
$541$	−14.6834	−	12.7232i	−0.631288	−	0.547014i	−0.910654	+	0.413171i	$0.864421\pi$
$542$	25.5756	+	4.49931i	1.09856	+	0.193262i
$543$	5.72375	+	12.5333i	0.245630	+	0.537854i
$544$	3.53075	−	22.3466i	0.151380	−	0.958101i
$545$	1.91933	+	0.563567i	0.0822152	+	0.0241406i
$546$	6.69836	−	20.4220i	0.286663	−	0.873982i
$547$	0.996632	+	0.455147i	0.0426129	+	0.0194607i	0.436607	−	0.899652i	$-0.356180\pi$
$547$	0.996632	+	0.455147i	0.0426129	+	0.0194607i	−0.393995	+	0.919113i	$0.628907\pi$
$548$	0.546864	−	0.304829i	0.0233609	−	0.0130216i
$549$	−6.75974	+	10.5184i	−0.288499	+	0.448913i
$550$	−39.1861	+	10.1838i	−1.67090	+	0.434239i
$551$	−4.70038			−0.200243
$552$	9.43728	−	9.74360i	0.401677	−	0.414715i
$553$	−5.98744			−0.254612
$554$	22.7321	−	5.90770i	0.965796	−	0.250994i
$555$	0.241926	−	0.376443i	0.0102692	−	0.0159791i
$556$	5.45411	+	9.78468i	0.231306	+	0.414963i
$557$	−3.16457	−	1.44521i	−0.134087	−	0.0612356i	0.347242	−	0.937776i	$-0.387118\pi$
$557$	−3.16457	−	1.44521i	−0.134087	−	0.0612356i	−0.481329	+	0.876540i	$0.659846\pi$
$558$	−0.129148	+	0.393748i	−0.00546728	+	0.0166687i
$559$	−33.2390	−	9.75985i	−1.40586	−	0.412798i
$560$	2.01002	−	0.628463i	0.0849387	−	0.0265574i
$561$	9.59662	+	21.0137i	0.405170	+	0.887198i
$562$	20.1149	+	3.53866i	0.848496	+	0.149270i
$563$	−16.2854	−	14.1113i	−0.686346	−	0.594722i	0.240281	−	0.970703i	$-0.422760\pi$
$563$	−16.2854	−	14.1113i	−0.686346	−	0.594722i	−0.926627	+	0.375981i	$0.877306\pi$
$564$	−0.394148	+	6.27984i	−0.0165966	+	0.264429i
$565$	0.543487	+	1.85095i	0.0228647	+	0.0778699i
$566$	8.20154	+	0.257127i	0.344736	+	0.0108079i
$567$	−2.12036	+	1.36267i	−0.0890467	+	0.0572268i
$568$	−3.13722	+	33.2683i	−0.131635	+	1.39591i
$569$	−0.432272	−	3.00652i	−0.0181218	−	0.126040i	0.978752	−	0.205046i	$-0.0657344\pi$
$569$	−0.432272	−	3.00652i	−0.0181218	−	0.126040i	−0.996874	+	0.0790062i	$0.974825\pi$
$570$	1.28645	+	1.58223i	0.0538836	+	0.0662721i
$571$	−10.0516	−	1.44520i	−0.420645	−	0.0604796i	−0.0712576	−	0.997458i	$-0.522701\pi$
$571$	−10.0516	−	1.44520i	−0.420645	−	0.0604796i	−0.349388	+	0.936978i	$0.613610\pi$
$572$	−5.57481	−	69.4337i	−0.233095	−	2.90317i
$573$	11.1372	−	9.65046i	0.465264	−	0.403154i
$574$	−36.2879	−	17.9671i	−1.51463	−	0.749931i
$575$	−23.0484	−	5.81182i	−0.961187	−	0.242370i
$576$	7.41992	−	2.99078i	0.309163	−	0.124616i
$577$	−0.302321	−	0.348897i	−0.0125858	−	0.0145248i	0.749422	−	0.662093i	$-0.230332\pi$
$577$	−0.302321	−	0.348897i	−0.0125858	−	0.0145248i	−0.762008	+	0.647568i	$0.775786\pi$
$578$	−0.730664	−	1.21932i	−0.0303916	−	0.0507172i
$579$	−18.8151	−	2.70520i	−0.781928	−	0.112424i
$580$	−0.277432	+	0.0628896i	−0.0115197	+	0.00261135i
$581$	−35.6999	+	5.13287i	−1.48108	+	0.212947i
$582$	5.91538	−	6.40936i	0.245200	−	0.265677i
$583$	12.4986	−	8.03237i	0.517640	−	0.332667i
$584$	26.3004	−	18.7752i	1.08832	−	0.776922i
$585$	1.20849	−	0.354844i	0.0499648	−	0.0146710i
$586$	2.30441	+	5.49545i	0.0951941	+	0.227015i
$587$	29.9501	+	25.9519i	1.23617	+	1.07115i	0.994918	+	0.100689i	$0.0321047\pi$
$587$	29.9501	+	25.9519i	1.23617	+	1.07115i	0.241256	+	0.970462i	$0.422441\pi$
$588$	0.766652	−	1.04296i	0.0316162	−	0.0430109i
$589$	−1.83990	+	0.840255i	−0.0758118	+	0.0346221i
$590$	2.26879	−	0.253929i	0.0934047	−	0.0104541i
$591$	−19.9673	−	5.86293i	−0.821345	−	0.241169i
$592$	1.07141	−	8.50159i	0.0440346	−	0.349413i
$593$	−5.40534	+	11.8360i	−0.221971	+	0.486048i	−0.987552	−	0.157291i	$-0.949724\pi$
$593$	−5.40534	+	11.8360i	−0.221971	+	0.486048i	0.765582	+	0.643339i	$0.222451\pi$
$594$	−4.62959	+	6.73031i	−0.189954	+	0.276148i
$595$	−1.13839	+	1.77138i	−0.0466696	+	0.0726193i
$596$	−4.32026	−	0.900441i	−0.176965	−	0.0368835i
$597$			16.4909i			0.674928i
$598$	16.7181	−	37.3214i	0.683656	−	1.52619i
$599$	18.0460			0.737340			0.368670	−	0.929560i	$-0.379813\pi$
$599$	18.0460			0.737340			0.368670	+	0.929560i	$0.379813\pi$
$600$	−11.0297	−	8.65282i	−0.450284	−	0.353250i
$601$	−0.411046	−	0.264163i	−0.0167669	−	0.0107754i	0.532231	−	0.846599i	$-0.321354\pi$
$601$	−0.411046	−	0.264163i	−0.0167669	−	0.0107754i	−0.548997	+	0.835824i	$0.684990\pi$
$602$	16.8728	+	11.6063i	0.687685	+	0.473039i
$603$	3.40741	+	1.55611i	0.138761	+	0.0633698i
$604$	33.6696	−	34.2619i	1.37000	−	1.39410i
$605$	−1.31619	+	4.48253i	−0.0535107	+	0.182241i
$606$	−17.4934	+	1.95790i	−0.710619	+	0.0795344i
$607$	3.73915	+	8.18759i	0.151767	+	0.332324i	0.970211	−	0.242263i	$-0.0778898\pi$
$607$	3.73915	+	8.18759i	0.151767	+	0.332324i	−0.818443	+	0.574587i	$0.805163\pi$
$608$	35.2914	+	16.7139i	1.43126	+	0.677840i
$609$	1.12390	−	1.29705i	0.0455427	−	0.0525591i
$610$	−3.40623	+	1.42833i	−0.137914	+	0.0578315i
$611$	5.34440	+	18.2013i	0.216211	+	0.736347i
$612$	−3.77203	+	7.05346i	−0.152475	+	0.285119i
$613$	−15.1375	−	23.5543i	−0.611396	−	0.951351i	−0.999557	−	0.0297591i	$-0.990526\pi$
$613$	−15.1375	−	23.5543i	−0.611396	−	0.951351i	0.388161	−	0.921592i	$-0.373110\pi$
$614$	−28.3537	+	30.7214i	−1.14426	+	1.23982i
$615$	−0.337705	−	2.34879i	−0.0136176	−	0.0947122i
$616$	−9.66115	+	40.0294i	−0.389259	+	1.61283i
$617$	6.03774	−	41.9934i	0.243070	−	1.69059i	−0.393462	−	0.919341i	$-0.628723\pi$
$617$	6.03774	−	41.9934i	0.243070	−	1.69059i	0.636532	−	0.771250i	$-0.280368\pi$
$618$	−14.0570	+	8.42348i	−0.565457	+	0.338842i
$619$	−13.1961	+	11.4345i	−0.530395	+	0.459590i	−0.878416	−	0.477897i	$-0.841399\pi$
$619$	−13.1961	+	11.4345i	−0.530395	+	0.459590i	0.348021	+	0.937487i	$0.386854\pi$
$620$	−0.0973546	+	0.0742119i	−0.00390986	+	0.00298042i
$621$	−4.28233	+	2.15909i	−0.171844	+	0.0866413i
$622$	33.5473	+	16.6101i	1.34512	+	0.666004i
$623$	−27.6490	−	31.9086i	−1.10773	−	1.27839i
$624$	17.9494	−	16.1096i	0.718549	−	0.644901i
$625$	−3.46500	+	24.0996i	−0.138600	+	0.963983i
$626$	−3.28524	+	2.67111i	−0.131304	+	0.106759i
$627$	−39.4675	+	5.67457i	−1.57618	+	0.226621i
$628$	−34.9183	+	13.3718i	−1.39339	+	0.533591i
$629$	4.63192	+	7.20740i	0.184687	+	0.287378i
$630$	−0.744209	−	0.0233318i	−0.0296500	−	0.000929562i
$631$	38.7533	−	11.3790i	1.54274	−	0.452991i	0.603822	−	0.797119i	$-0.293644\pi$
$631$	38.7533	−	11.3790i	1.54274	−	0.452991i	0.938922	+	0.344129i	$0.111826\pi$
$632$	−5.82277	−	3.35264i	−0.231617	−	0.133361i
$633$	1.86114	−	2.14787i	0.0739735	−	0.0853700i
$634$	−1.26721	+	7.20324i	−0.0503274	+	0.286077i
$635$	1.65010	−	0.753575i	0.0654821	−	0.0299047i
$636$	4.83536	+	1.75563i	0.191734	+	0.0696153i
$637$	1.09944	−	3.74434i	0.0435613	−	0.148356i
$638$	1.73356	−	5.28530i	0.0686323	−	0.209247i
$639$	4.90784	−	10.7467i	0.194151	−	0.425131i
$640$	2.30664	+	0.514323i	0.0911780	+	0.0203304i
$641$	20.6635	+	13.2796i	0.816158	+	0.524513i	0.880852	−	0.473392i	$-0.156971\pi$
$641$	20.6635	+	13.2796i	0.816158	+	0.524513i	−0.0646939	+	0.997905i	$0.520607\pi$
$642$	1.76365	+	6.78633i	0.0696057	+	0.267835i
$643$			11.8132i			0.465866i	0.972493	+	0.232933i	$0.0748323\pi$
$643$			11.8132i			0.465866i	−0.972493	+	0.232933i	$0.925168\pi$
$644$	−16.2671	+	17.8840i	−0.641014	+	0.704729i
$645$			1.20013i			0.0472550i
$646$	−37.7877	+	9.82038i	−1.48674	+	0.386378i
$647$	−15.6174	−	10.0367i	−0.613985	−	0.394584i	0.196364	−	0.980531i	$-0.437086\pi$
$647$	−15.6174	−	10.0367i	−0.613985	−	0.394584i	−0.810350	+	0.585947i	$0.800723\pi$
$648$	−2.82506	+	0.137908i	−0.110979	+	0.00541752i
$649$	−18.5438	+	40.6054i	−0.727910	+	1.59390i
$650$	−40.1587	−	13.1719i	−1.57515	−	0.516646i
$651$	0.208071	−	0.708624i	0.00815494	−	0.0277732i
$652$	−1.23650	+	3.40558i	−0.0484252	+	0.133373i
$653$	9.25563	−	4.22690i	0.362201	−	0.165411i	−0.225998	−	0.974128i	$-0.572564\pi$
$653$	9.25563	−	4.22690i	0.362201	−	0.165411i	0.588199	+	0.808716i	$0.299837\pi$
$654$	−13.3381	−	2.34647i	−0.521561	−	0.0917543i
$655$	0.857513	−	0.989622i	0.0335058	−	0.0386677i
$656$	−25.2293	−	37.7922i	−0.985039	−	1.47554i
$657$	−10.9621	+	3.21876i	−0.427671	+	0.125576i
$658$	0.351406	−	11.2087i	0.0136992	−	0.436961i
$659$	−0.122174	−	0.190106i	−0.00475921	−	0.00740547i	0.838866	−	0.544338i	$-0.183219\pi$
$659$	−0.122174	−	0.190106i	−0.00475921	−	0.00740547i	−0.843625	+	0.536933i	$0.819583\pi$
$660$	−2.25358	+	0.862994i	−0.0877204	+	0.0335920i
$661$	−14.2576	+	2.04994i	−0.554558	+	0.0797334i	−0.413896	−	0.910324i	$-0.635832\pi$
$661$	−14.2576	+	2.04994i	−0.554558	+	0.0797334i	−0.140662	+	0.990058i	$0.544923\pi$
$662$	18.1599	+	22.3351i	0.705806	+	0.868079i
$663$	−3.43186	+	23.8691i	−0.133282	+	0.927000i
$664$	−37.5922	−	14.9983i	−1.45886	−	0.582047i
$665$	−2.38001	−	2.74668i	−0.0922930	−	0.106512i
$666$	−1.34425	+	2.71498i	−0.0520887	+	0.105203i
$667$	2.38361	−	2.23213i	0.0922939	−	0.0864283i
$668$	5.04263	+	6.61516i	0.195105	+	0.255948i
$669$	6.74146	−	5.84150i	0.260640	−	0.225846i
$670$	0.568801	+	0.949209i	0.0219747	+	0.0366712i
$671$	10.2782	−	71.4865i	0.396786	−	2.75970i
$672$	−13.0506	+	5.74207i	−0.503438	+	0.221505i
$673$	−1.01054	−	7.02849i	−0.0389536	−	0.270928i	0.961031	−	0.276440i	$-0.0891547\pi$
$673$	−1.01054	−	7.02849i	−0.0389536	−	0.270928i	−0.999985	+	0.00551154i	$0.998246\pi$
$674$	21.1026	+	19.4762i	0.812840	+	0.750193i
$675$	2.67961	+	4.16956i	0.103138	+	0.160486i
$676$	22.0286	−	41.1921i	0.847254	−	1.58431i
$677$	6.29145	+	21.4267i	0.241800	+	0.823495i	0.987555	+	0.157275i	$0.0502708\pi$
$677$	6.29145	+	21.4267i	0.241800	+	0.823495i	−0.745755	+	0.666220i	$0.767911\pi$
$678$	−5.05054	−	12.0443i	−0.193965	−	0.462559i
$679$	−10.1795	+	11.7478i	−0.390654	+	0.450839i
$680$	−2.09896	+	1.08522i	−0.0804914	+	0.0416162i
$681$	−1.74214	−	3.81475i	−0.0667588	−	0.146181i
$682$	−0.266236	−	2.37875i	−0.0101947	−	0.0910872i
$683$	−3.42492	+	11.6642i	−0.131051	+	0.446318i	−0.998706	−	0.0508475i	$-0.983808\pi$
$683$	−3.42492	+	11.6642i	−0.131051	+	0.446318i	0.867656	+	0.497166i	$0.165626\pi$
$684$	−9.84703	−	9.67682i	−0.376511	−	0.370002i
$685$	−0.0594811	−	0.0271641i	−0.00227266	−	0.00103789i
$686$	−15.4483	+	22.4582i	−0.589820	+	0.857457i
$687$	2.63968	+	1.69642i	0.100710	+	0.0647225i
$688$	9.90985	+	20.7350i	0.377810	+	0.790515i
$689$	15.5088			0.590839
$690$	−1.40374	−	0.191450i	−0.0534396	−	0.00728837i
$691$		−	11.4682i		−	0.436270i	−0.975919	−	0.218135i	$-0.930003\pi$
$691$		−	11.4682i		−	0.436270i	0.975919	−	0.218135i	$-0.0699974\pi$
$692$	34.5809	+	7.20746i	1.31457	+	0.273987i
$693$	7.87113	−	12.2477i	0.299000	−	0.465252i
$694$	10.3776	+	7.13846i	0.393929	+	0.270972i
$695$	0.486030	−	1.06426i	0.0184362	−	0.0403696i
$696$	1.81927	−	0.632053i	0.0689591	−	0.0239579i
$697$	43.5921	+	12.7998i	1.65117	+	0.484827i
$698$	1.95254	+	17.4455i	0.0739048	+	0.660321i
$699$	−5.51867	+	2.52029i	−0.208735	+	0.0953262i
$700$	20.1311	+	14.7979i	0.760885	+	0.559307i
$701$	9.31667	+	8.07294i	0.351886	+	0.304911i	0.812810	−	0.582529i	$-0.197937\pi$
$701$	9.31667	+	8.07294i	0.351886	+	0.304911i	−0.460924	+	0.887439i	$0.652482\pi$
$702$	−7.86377	+	3.29751i	−0.296799	+	0.124457i
$703$	−14.1886	+	4.16616i	−0.535134	+	0.157130i
$704$	−31.8097	+	33.5187i	−1.19887	+	1.26328i
$705$	0.552854	−	0.355298i	0.0208217	−	0.0133813i
$706$	−5.00523	−	4.61947i	−0.188374	−	0.173856i
$707$	31.0528	−	4.46472i	1.16786	−	0.167913i
$708$	−15.0737	+	3.41699i	−0.566505	+	0.128418i
$709$	14.9934	+	2.15572i	0.563088	+	0.0809598i	0.417980	−	0.908456i	$-0.362738\pi$
$709$	14.9934	+	2.15572i	0.563088	+	0.0809598i	0.145108	+	0.989416i	$0.453647\pi$
$710$	2.99372	−	1.79394i	0.112352	−	0.0673255i
$711$	1.55564	+	1.79530i	0.0583409	+	0.0673290i
$712$	−9.02143	−	46.5129i	−0.338093	−	1.74315i
$713$	0.534012	−	1.29984i	0.0199989	−	0.0486793i
$714$	6.32545	−	12.7755i	0.236724	−	0.478110i
$715$	−5.49825	+	4.76426i	−0.205623	+	0.178173i
$716$	−21.2520	+	1.70632i	−0.794224	+	0.0637681i
$717$	0.489097	+	0.0703216i	0.0182657	+	0.00262621i
$718$	−1.73177	+	1.40804i	−0.0646291	+	0.0525477i
$719$	3.62904	+	25.2405i	0.135340	+	0.941313i	0.938434	+	0.345460i	$0.112277\pi$
$719$	3.62904	+	25.2405i	0.135340	+	0.941313i	−0.803093	+	0.595853i	$0.796814\pi$
$720$	−0.710677	−	0.439407i	−0.0264854	−	0.0163757i
$721$	24.5703	−	15.7904i	0.915047	−	0.588065i
$722$	1.26969	−	40.4991i	0.0472530	−	1.50722i
$723$	−4.69211	−	15.9799i	−0.174502	−	0.594298i
$724$	1.72618	−	27.5027i	0.0641528	−	1.02213i
$725$	−2.55057	−	2.21008i	−0.0947259	−	0.0820804i
$726$	5.48009	−	31.1506i	0.203385	−	1.15611i
$727$	10.8370	+	23.7298i	0.401924	+	0.880090i	0.997072	+	0.0764737i	$0.0243661\pi$
$727$	10.8370	+	23.7298i	0.401924	+	0.880090i	−0.595148	+	0.803616i	$0.702907\pi$
$728$	−31.0747	+	29.6996i	−1.15171	+	1.10074i
$729$	0.959493	+	0.281733i	0.0355368	+	0.0104345i
$730$	−3.20693	−	1.05186i	−0.118694	−	0.0389312i
$731$	−20.9013	−	9.54529i	−0.773061	−	0.353045i
$732$	21.8423	−	12.1752i	0.807314	−	0.450007i
$733$	25.5647	−	39.7795i	0.944255	−	1.46929i	0.0622441	−	0.998061i	$-0.480174\pi$
$733$	25.5647	−	39.7795i	0.944255	−	1.46929i	0.882011	−	0.471229i	$-0.156189\pi$
$734$	−3.18958	−	12.2731i	−0.117729	−	0.453009i
$735$	−0.135193			−0.00498669
$736$	−25.8338	+	8.28343i	−0.952246	+	0.305331i
$737$	−21.6374			−0.797024
$738$	4.04089	+	15.5489i	0.148747	+	0.572362i
$739$	−3.49616	+	5.44013i	−0.128608	+	0.200119i	−0.899586	−	0.436744i	$-0.856132\pi$
$739$	−3.49616	+	5.44013i	−0.128608	+	0.200119i	0.770978	+	0.636862i	$0.219768\pi$
$740$	−0.781717	+	0.435739i	−0.0287365	+	0.0160181i
$741$	−37.8610	−	17.2905i	−1.39086	−	0.635184i
$742$	−8.71161	−	2.85738i	−0.319813	−	0.104898i
$743$	21.9447	+	6.44355i	0.805074	+	0.236391i	0.658277	−	0.752776i	$-0.271286\pi$
$743$	21.9447	+	6.44355i	0.805074	+	0.236391i	0.146797	+	0.989167i	$0.453104\pi$
$744$	0.599139	−	0.572626i	0.0219655	−	0.0209935i
$745$	0.191473	+	0.419267i	0.00701501	+	0.0153607i
$746$	0.849003	−	4.82601i	0.0310842	−	0.176693i
$747$	10.8145	+	9.37080i	0.395681	+	0.342860i
$748$	2.89416	−	46.1118i	0.105821	−	1.68602i
$749$	−3.52072	−	11.9905i	−0.128644	−	0.438122i
$750$	−0.0921652	+	2.93977i	−0.00336540	+	0.107345i
$751$	32.9771	−	21.1931i	1.20335	−	0.773346i	0.223818	−	0.974631i	$-0.428148\pi$
$751$	32.9771	−	21.1931i	1.20335	−	0.773346i	0.979533	+	0.201285i	$0.0645116\pi$
$752$	6.61802	−	10.7037i	0.241334	−	0.390323i
$753$	−3.17007	−	22.0483i	−0.115524	−	0.803485i
$754$	4.50511	−	3.66296i	0.164067	−	0.133397i
$755$	−4.96605	−	0.714010i	−0.180733	−	0.0259855i
$756$	5.02478	−	0.403438i	0.182749	−	0.0146729i
$757$	20.6418	−	17.8862i	0.750240	−	0.650087i	−0.193378	−	0.981124i	$-0.561944\pi$
$757$	20.6418	−	17.8862i	0.750240	−	0.650087i	0.943617	+	0.331038i	$0.107399\pi$
$758$	−4.71412	+	9.52107i	−0.171225	+	0.345821i
$759$	17.3196	−	21.6200i	0.628663	−	0.784758i
$760$	−0.776562	−	4.00382i	−0.0281689	−	0.145234i
$761$	−11.6373	−	13.4302i	−0.421852	−	0.486844i	0.504548	−	0.863384i	$-0.331659\pi$
$761$	−11.6373	−	13.4302i	−0.421852	−	0.486844i	−0.926400	+	0.376540i	$0.877114\pi$
$762$	−10.5348	+	6.31281i	−0.381634	+	0.228689i
$763$	23.8911	+	3.43503i	0.864917	+	0.124356i
$764$	−28.7440	+	6.51584i	−1.03992	+	0.235735i
$765$	0.826910	−	0.118892i	0.0298970	−	0.00429854i
$766$	8.52732	+	7.87010i	0.308105	+	0.284358i
$767$	−39.2002	+	25.1924i	−1.41544	+	0.909646i
$768$	−15.9069	−	1.72349i	−0.573991	−	0.0621910i
$769$	−3.69461	+	1.08484i	−0.133231	+	0.0391202i	−0.347668	−	0.937618i	$-0.613026\pi$
$769$	−3.69461	+	1.08484i	−0.133231	+	0.0391202i	0.214437	+	0.976738i	$0.431208\pi$
$770$	3.96626	−	1.66317i	0.142934	−	0.0599365i
$771$	−12.4969	−	10.8286i	−0.450064	−	0.389983i
$772$	30.6317	+	22.5166i	1.10246	+	0.810391i
$773$	−35.4864	+	16.2061i	−1.27636	+	0.582894i	−0.934200	−	0.356749i	$-0.883885\pi$
$773$	−35.4864	+	16.2061i	−1.27636	+	0.582894i	−0.342158	+	0.939642i	$0.611158\pi$
$774$	−0.903746	−	8.07474i	−0.0324845	−	0.290241i
$775$	−1.39347	−	0.409159i	−0.0500549	−	0.0146974i
$776$	−16.4777	+	5.72471i	−0.591515	+	0.205505i
$777$	2.24298	−	4.91145i	0.0804666	−	0.176197i
$778$	30.5766	+	21.0328i	1.09623	+	0.754062i
$779$	−42.3957	+	65.9690i	−1.51898	+	2.36358i
$780$	−2.46602	−	0.513976i	−0.0882977	−	0.0184033i
$781$			68.2423i			2.44190i
$782$	14.4990	−	22.9247i	0.518484	−	0.819786i
$783$	−0.680920			−0.0243341
$784$	−2.33578	+	1.11634i	−0.0834207	+	0.0398691i
$785$	3.28531	+	2.11134i	0.117258	+	0.0753569i
$786$	−5.02431	+	7.30415i	−0.179211	+	0.260530i
$787$	−9.90130	−	4.52177i	−0.352943	−	0.161184i	0.231051	−	0.972942i	$-0.425784\pi$
$787$	−9.90130	−	4.52177i	−0.352943	−	0.161184i	−0.583994	+	0.811758i	$0.698511\pi$
$788$	29.6856	+	29.1725i	1.05751	+	1.03923i
$789$	2.30128	−	7.83744i	0.0819277	−	0.279020i
$790$	0.0780549	+	0.697400i	0.00277707	+	0.0248124i
$791$	9.66952	+	21.1733i	0.343809	+	0.752836i
$792$	14.5127	−	7.50346i	0.515687	−	0.266624i
$793$	49.3696	−	56.9755i	1.75316	−	2.02326i
$794$	14.7178	+	35.0984i	0.522316	+	1.24560i
$795$	−0.151369	−	0.515516i	−0.00536851	−	0.0182835i
$796$	15.5535	−	29.0842i	0.551281	−	1.03086i
$797$	4.64398	+	7.22618i	0.164498	+	0.255964i	0.913711	−	0.406366i	$-0.133204\pi$
$797$	4.64398	+	7.22618i	0.164498	+	0.255964i	−0.749212	+	0.662330i	$0.769568\pi$
$798$	18.0816	+	16.6881i	0.640083	+	0.590751i
$799$	1.79066	+	12.4543i	0.0633489	+	0.440601i
$800$	11.2914	+	25.6632i	0.399213	+	0.907332i
$801$	−2.38395	+	16.5808i	−0.0842329	+	0.585853i
$802$	−6.06440	−	10.1202i	−0.214141	−	0.357357i
$803$	49.8741	−	43.2161i	1.76002	−	1.52506i
$804$	−4.54181	−	5.95816i	−0.160177	−	0.210128i
$805$	2.51128	+	0.262647i	0.0885110	+	0.00925708i
$806$	1.10866	−	2.23916i	0.0390511	−	0.0788711i
$807$	−9.95776	−	11.4919i	−0.350530	−	0.404533i
$808$	32.6987	+	13.0460i	1.15034	+	0.458955i
$809$	0.995509	−	6.92392i	0.0350002	−	0.243432i	−0.964809	−	0.262951i	$-0.915304\pi$
$809$	0.995509	−	6.92392i	0.0350002	−	0.243432i	0.999809	+	0.0195188i	$0.00621341\pi$
$810$	0.186362	+	0.229209i	0.00654809	+	0.00805358i
$811$	12.3166	−	1.77086i	0.432495	−	0.0621834i	0.0773707	−	0.997002i	$-0.475348\pi$
$811$	12.3166	−	1.77086i	0.432495	−	0.0621834i	0.355125	+	0.934819i	$0.384438\pi$
$812$	−3.20549	+	1.22752i	−0.112490	+	0.0430776i
$813$	9.92744	+	15.4474i	0.348171	+	0.541764i
$814$	0.548356	−	17.4908i	0.0192199	−	0.613052i
$815$	0.363082	−	0.106610i	0.0127182	−	0.00373440i
$816$	13.3051	−	8.88219i	0.465770	−	0.310939i
$817$	25.9718	−	29.9731i	0.908640	−	1.04863i
$818$	22.5777	+	3.97192i	0.789409	+	0.138875i
$819$	13.8241	−	6.31326i	0.483054	−	0.220603i
$820$	−1.61969	+	4.46094i	−0.0565619	+	0.155783i
$821$	−1.59913	+	5.44614i	−0.0558100	+	0.190072i	−0.982680	−	0.185311i	$-0.940671\pi$
$821$	−1.59913	+	5.44614i	−0.0558100	+	0.190072i	0.926870	+	0.375383i	$0.122489\pi$
$822$	0.420658	+	0.137975i	0.0146721	+	0.00481242i
$823$	3.10014	−	6.78837i	0.108064	−	0.236628i	−0.847873	−	0.530200i	$-0.822117\pi$
$823$	3.10014	−	6.78837i	0.108064	−	0.236628i	0.955937	+	0.293572i	$0.0948441\pi$
$824$	32.7363	−	1.59805i	1.14042	−	0.0556707i
$825$	−24.0844	−	15.4781i	−0.838512	−	0.538879i
$826$	26.6610	−	6.92875i	0.927656	−	0.241082i
$827$		−	1.48225i		−	0.0515429i	−0.999668	−	0.0257715i	$-0.991796\pi$
$827$		−	1.48225i		−	0.0515429i	0.999668	−	0.0257715i	$-0.00820422\pi$
$828$	9.58888	+	0.231041i	0.333237	+	0.00802922i
$829$		−	34.1951i		−	1.18764i	−0.804597	−	0.593822i	$-0.797618\pi$
$829$		−	34.1951i		−	1.18764i	0.804597	−	0.593822i	$-0.202382\pi$
$830$	1.06326	+	4.09131i	0.0369063	+	0.142011i
$831$	13.9715	+	8.97896i	0.484667	+	0.311477i
$832$	−46.8503	+	11.4826i	−1.62424	+	0.398088i
$833$	1.07527	−	2.35451i	0.0372558	−	0.0815789i
$834$	−2.46869	+	7.52657i	−0.0854838	+	0.260624i
$835$	0.244757	−	0.833566i	0.00847017	−	0.0288467i
$836$	74.9588	+	27.2162i	2.59251	+	0.941291i
$837$	−0.266537	+	0.121723i	−0.00921287	+	0.00420738i
$838$	−2.94435	+	16.7367i	−0.101711	+	0.578158i
$839$	−12.3653	+	14.2703i	−0.426898	+	0.492666i	−0.927926	−	0.372765i	$-0.878410\pi$
$839$	−12.3653	+	14.2703i	−0.426898	+	0.492666i	0.501028	+	0.865431i	$0.332955\pi$
$840$	1.29052	+	0.743056i	0.0445271	+	0.0256379i
$841$	−27.3804	+	8.03962i	−0.944153	+	0.277228i
$842$	33.8558	+	1.06142i	1.16675	+	0.0365789i
$843$	7.80783	+	12.1492i	0.268916	+	0.418442i
$844$	−5.30816	+	2.03273i	−0.182715	+	0.0699695i
$845$	−4.82915	+	0.694327i	−0.166128	+	0.0238856i
$846$	−3.45217	+	2.80684i	−0.118688	+	0.0965013i
$847$	−8.02237	+	55.7968i	−0.275652	+	1.91720i
$848$	−6.87203	−	7.65682i	−0.235987	−	0.262936i
$849$	3.79964	+	4.38502i	0.130403	+	0.150493i
$850$	−25.1222	−	12.4386i	−0.861685	−	0.426642i
$851$	5.21677	−	8.85062i	0.178829	−	0.303396i
$852$	−18.7915	+	14.3245i	−0.643786	+	0.490748i
$853$	21.1648	−	18.3394i	0.724668	−	0.627928i	−0.212357	−	0.977192i	$-0.568114\pi$
$853$	21.1648	−	18.3394i	0.724668	−	0.627928i	0.937024	+	0.349264i	$0.113568\pi$
$854$	−38.2292	+	22.9083i	−1.30818	+	0.783907i
$855$	−0.205210	+	1.42727i	−0.00701803	+	0.0488115i
$856$	3.29012	−	13.6321i	0.112454	−	0.465935i
$857$	1.32436	+	9.21115i	0.0452394	+	0.314647i	0.999859	+	0.0168177i	$0.00535348\pi$
$857$	1.32436	+	9.21115i	0.0452394	+	0.314647i	−0.954619	+	0.297829i	$0.903737\pi$
$858$	33.4058	−	36.1954i	1.14045	−	1.23569i
$859$	−12.9257	−	20.1128i	−0.441019	−	0.686238i	0.547590	−	0.836747i	$-0.315545\pi$
$859$	−12.9257	−	20.1128i	−0.441019	−	0.686238i	−0.988609	+	0.150508i	$0.951909\pi$
$860$	1.13191	−	2.11660i	0.0385979	−	0.0721756i
$861$	−8.06668	−	27.4726i	−0.274912	−	0.936264i
$862$	−12.7902	+	5.36330i	−0.435635	+	0.182675i
$863$	36.3504	−	41.9506i	1.23738	−	1.42801i	0.370998	−	0.928634i	$-0.379016\pi$
$863$	36.3504	−	41.9506i	1.23738	−	1.42801i	0.866383	−	0.499380i	$-0.166439\pi$
$864$	5.11248	+	2.42126i	0.173930	+	0.0823730i
$865$	−1.53262	−	3.35596i	−0.0521106	−	0.114106i
$866$	9.15843	−	1.02504i	0.311216	−	0.0348321i
$867$	0.283181	−	0.964427i	0.00961734	−	0.0327537i
$868$	−1.03531	+	1.05352i	−0.0351407	+	0.0357588i
$869$	−12.4816	−	5.70016i	−0.423410	−	0.193365i
$870$	−0.165728	−	0.114000i	−0.00561871	−	0.00386495i
$871$	−19.0009	−	12.2112i	−0.643823	−	0.413760i
$872$	21.3106	+	16.7183i	0.721668	+	0.566153i
$873$	6.16732			0.208732
$874$	30.9152	+	35.1597i	1.04572	+	1.18929i
$875$		−	5.24197i		−	0.177211i
$876$	22.3690	+	4.66222i	0.755780	+	0.157522i
$877$	12.4730	−	19.4084i	0.421185	−	0.655377i	−0.564216	−	0.825627i	$-0.690821\pi$
$877$	12.4730	−	19.4084i	0.421185	−	0.655377i	0.985401	+	0.170251i	$0.0544578\pi$
$878$	−19.1662	+	27.8630i	−0.646828	+	0.940332i
$879$	−1.75043	+	3.83290i	−0.0590404	+	0.129281i
$880$	4.78846	+	0.603462i	0.161419	+	0.0203427i
$881$	24.5128	+	7.19759i	0.825856	+	0.242493i	0.667236	−	0.744847i	$-0.267477\pi$
$881$	24.5128	+	7.19759i	0.825856	+	0.242493i	0.158620	+	0.987340i	$0.449296\pi$
$882$	0.909612	−	0.101806i	0.0306282	−	0.00342799i
$883$	14.9132	−	6.81063i	0.501869	−	0.229196i	−0.148361	−	0.988933i	$-0.547400\pi$
$883$	14.9132	−	6.81063i	0.501869	−	0.229196i	0.650230	+	0.759737i	$0.274673\pi$
$884$	28.5650	−	38.8599i	0.960743	−	1.30700i
$885$	1.22000	+	1.05714i	0.0410099	+	0.0355353i
$886$	2.78058	+	6.63102i	0.0934155	+	0.222773i
$887$	1.01442	−	0.297862i	0.0340610	−	0.0100012i	−0.264658	−	0.964342i	$-0.585259\pi$
$887$	1.01442	−	0.297862i	0.0340610	−	0.0100012i	0.298719	+	0.954341i	$0.403441\pi$
$888$	4.93144	−	3.52042i	0.165488	−	0.118138i
$889$	18.4137	−	11.8338i	0.617577	−	0.396893i
$890$	−3.35618	+	3.63645i	−0.112499	+	0.121894i
$891$	−5.71746	+	0.822046i	−0.191542	+	0.0275396i
$892$	−17.3990	+	3.94409i	−0.582562	+	0.132058i
$893$	−21.4964	−	3.09072i	−0.719350	−	0.103427i
$894$	−1.60400	−	2.67673i	−0.0536456	−	0.0895233i
$895$	1.45823	+	1.68288i	0.0487432	+	0.0562526i
$896$	28.4323	+	2.18180i	0.949857	+	0.0728888i
$897$	27.4107	−	9.21128i	0.915216	−	0.307556i
$898$	−10.3546	−	5.12683i	−0.345538	−	0.171085i
$899$	0.150788	−	0.130658i	0.00502905	−	0.00435770i
$900$	−0.793338	−	9.88094i	−0.0264446	−	0.329365i
$901$	10.1821	+	1.46396i	0.339214	+	0.0487716i
$902$	−58.5420	−	72.0015i	−1.94924	−	2.39739i
$903$	2.06086	+	14.3336i	0.0685813	+	0.476993i
$904$	−2.45232	+	26.0054i	−0.0815631	+	0.864926i
$905$	−2.42123	+	1.55603i	−0.0804845	+	0.0517242i
$906$	33.9504	+	1.06438i	1.12793	+	0.0353618i
$907$	−7.08244	−	24.1206i	−0.235169	−	0.800910i	−0.989515	−	0.144433i	$-0.953864\pi$
$907$	−7.08244	−	24.1206i	−0.235169	−	0.800910i	0.754346	−	0.656477i	$-0.227954\pi$
$908$	−0.525396	+	8.37098i	−0.0174359	+	0.277801i
$909$	−9.40674	−	8.15099i	−0.312002	−	0.270351i
$910$	4.42160	+	0.777858i	0.146575	+	0.0257858i
$911$	21.6016	+	47.3008i	0.715692	+	1.56715i	0.819845	+	0.572585i	$0.194059\pi$
$911$	21.6016	+	47.3008i	0.715692	+	1.56715i	−0.104154	+	0.994561i	$0.533213\pi$
$912$	8.23992	+	26.3538i	0.272851	+	0.872662i
$913$	−79.3077	−	23.2869i	−2.62470	−	0.770682i
$914$	10.1704	−	31.0076i	0.336407	−	1.02564i
$915$	−2.37573	−	1.08496i	−0.0785394	−	0.0358677i
$916$	−3.05547	−	5.48153i	−0.100956	−	0.181115i
$917$	8.54224	−	13.2920i	0.282089	−	0.438940i
$918$	−5.47411	+	1.42263i	−0.180672	+	0.0469537i
$919$	24.8732			0.820490			0.410245	−	0.911975i	$-0.365443\pi$
$919$	24.8732			0.820490			0.410245	+	0.911975i	$0.365443\pi$
$920$	2.29514	+	1.66160i	0.0756686	+	0.0547814i
$921$	−29.5613			−0.974076
$922$	−25.5793	+	6.64761i	−0.842408	+	0.218928i
$923$	−38.5129	+	59.9272i	−1.26767	+	1.97253i
$924$	−25.4334	+	14.1769i	−0.836699	+	0.466387i
$925$	−9.65808	−	4.41070i	−0.317556	−	0.145023i
$926$	15.8292	−	48.2600i	0.520178	−	1.58592i
$927$	−11.1184	−	3.26467i	−0.365177	−	0.107226i
$928$	−3.80467	−	0.601137i	−0.124894	−	0.0197333i
$929$	6.53377	+	14.3070i	0.214366	+	0.469396i	0.986016	−	0.166651i	$-0.0532954\pi$
$929$	6.53377	+	14.3070i	0.214366	+	0.469396i	−0.771650	+	0.636048i	$0.780568\pi$
$930$	−0.0852510	−	0.0149976i	−0.00279549	−	0.000491789i
$931$	3.37644	+	2.92570i	0.110658	+	0.0958861i
$932$	12.1100	+	0.760073i	0.396677	+	0.0248970i
$933$	7.45745	+	25.3977i	0.244146	+	0.831485i
$934$	5.22632	+	0.163851i	0.171010	+	0.00536137i
$935$	−4.05952	+	2.60889i	−0.132760	+	0.0853199i
$936$	16.9790	+	1.60113i	0.554976	+	0.0523346i
$937$	1.10766	+	7.70394i	0.0361857	+	0.251677i	0.999883	−	0.0153217i	$-0.00487724\pi$
$937$	1.10766	+	7.70394i	0.0361857	+	0.251677i	−0.963697	+	0.266998i	$0.913968\pi$
$938$	8.42340	+	10.3600i	0.275034	+	0.338267i
$939$	−2.96349	−	0.426085i	−0.0967098	−	0.0139048i
$940$	−1.31014	+	0.105191i	−0.0427321	+	0.00343095i
$941$	4.62640	−	4.00880i	0.150816	−	0.130683i	−0.576185	−	0.817320i	$-0.695459\pi$
$941$	4.62640	−	4.00880i	0.150816	−	0.130683i	0.727001	+	0.686637i	$0.240914\pi$
$942$	−23.6942	−	11.7316i	−0.771999	−	0.382236i
$943$	−9.82816	−	53.5865i	−0.320049	−	1.74502i
$944$	29.8075	+	8.19055i	0.970151	+	0.266580i
$945$	−0.344780	−	0.397898i	−0.0112157	−	0.0129436i
$946$	24.1242	+	40.2582i	0.784345	+	1.30891i
$947$	16.5999	+	2.38671i	0.539424	+	0.0775575i	0.406642	−	0.913588i	$-0.366700\pi$
$947$	16.5999	+	2.38671i	0.539424	+	0.0775575i	0.132783	+	0.991145i	$0.457609\pi$
$948$	−1.05034	−	4.63349i	−0.0341135	−	0.150489i
$949$	68.1863	−	9.80371i	2.21342	−	0.318242i
$950$	32.8161	−	35.5565i	1.06469	−	1.15360i
$951$	−4.35069	+	2.79602i	−0.141081	+	0.0906672i
$952$	−23.2052	+	16.5655i	−0.752084	+	0.536892i
$953$	−21.7018	+	6.37224i	−0.702992	+	0.206417i	−0.613643	−	0.789583i	$-0.710297\pi$
$953$	−21.7018	+	6.37224i	−0.702992	+	0.206417i	−0.0893485	+	0.996000i	$0.528478\pi$
$954$	1.40665	+	3.35452i	0.0455420	+	0.108607i
$955$	2.32642	+	2.01585i	0.0752812	+	0.0652315i
$956$	−0.796271	−	0.585319i	−0.0257532	−	0.0189306i
$957$	3.57773	−	1.63390i	0.115652	−	0.0528164i
$958$	53.1109	−	5.94431i	1.71593	−	0.192052i
$959$	−0.757053	−	0.222291i	−0.0244465	−	0.00717814i
$960$	0.838952	+	1.44524i	0.0270771	+	0.0466449i
$961$	−12.8422	+	28.1205i	−0.414264	+	0.907113i
$962$	10.3525	−	15.0501i	0.333780	−	0.485235i
$963$	−2.68053	+	4.17098i	−0.0863788	+	0.134408i
$964$	−6.79632	+	32.6083i	−0.218895	+	1.05024i
$965$		−	3.97064i		−	0.127819i
$966$	−17.0942	+	0.123951i	−0.549998	+	0.00398805i
$967$	−36.6351			−1.17810			−0.589052	−	0.808095i	$-0.700499\pi$
$967$	−36.6351			−1.17810			−0.589052	+	0.808095i	$0.700499\pi$
$968$	−39.0449	+	49.7701i	−1.25495	+	1.59967i
$969$	−23.2249	−	14.9257i	−0.746092	−	0.479484i
$970$	1.50106	+	1.03253i	0.0481960	+	0.0331526i
$971$	−17.3842	−	7.93909i	−0.557885	−	0.254777i	0.116458	−	0.993196i	$-0.462846\pi$
$971$	−17.3842	−	7.93909i	−0.557885	−	0.254777i	−0.674343	+	0.738418i	$0.735573\pi$
$972$	−1.42649	−	1.40183i	−0.0457547	−	0.0449637i
$973$	3.97731	−	13.5455i	0.127507	−	0.434248i
$974$	28.8453	−	3.22845i	0.924264	−	0.103446i
$975$	−12.4147	−	27.1843i	−0.397587	−	0.870595i
$976$	−50.0052	+	0.871987i	−1.60063	+	0.0279116i
$977$	−9.38645	+	10.8325i	−0.300299	+	0.346564i	−0.885765	−	0.464133i	$-0.846366\pi$
$977$	−9.38645	+	10.8325i	−0.300299	+	0.346564i	0.585466	+	0.810697i	$0.300911\pi$
$978$	−2.36261	+	0.990714i	−0.0755480	+	0.0316795i
$979$	−27.2603	−	92.8401i	−0.871243	−	2.96718i
$980$	0.238434	+	0.127509i	0.00761648	+	0.00407312i
$981$	−5.17734	−	8.05609i	−0.165300	−	0.257211i
$982$	4.05285	−	4.39129i	0.129332	−	0.140132i
$983$	−5.61170	−	39.0302i	−0.178985	−	1.24487i	−0.859117	−	0.511780i	$-0.828986\pi$
$983$	−5.61170	−	39.0302i	−0.178985	−	1.24487i	0.680131	−	0.733090i	$-0.261923\pi$
$984$	7.53835	−	31.2339i	0.240314	−	0.995701i
$985$	0.618641	−	4.30275i	0.0197116	−	0.137097i
$986$	3.30353	−	1.97960i	0.105206	−	0.0630432i
$987$	5.99284	−	5.19282i	0.190754	−	0.165289i
$988$	50.4657	+	66.2033i	1.60553	+	2.10621i
$989$	1.06308	+	27.5332i	0.0338041	+	0.875506i
$990$	−1.52919	−	0.757140i	−0.0486009	−	0.0240635i
$991$	−14.7563	−	17.0296i	−0.468748	−	0.540964i	0.471315	−	0.881965i	$-0.343780\pi$
$991$	−14.7563	−	17.0296i	−0.468748	−	0.540964i	−0.940063	+	0.341001i	$0.889234\pi$
$992$	−1.59675	+	0.444827i	−0.0506968	+	0.0141233i
$993$	−2.89680	+	20.1477i	−0.0919271	+	0.639367i
$994$	32.6746	−	26.5666i	1.03638	−	0.842642i
$995$	−3.40967	+	0.490237i	−0.108094	+	0.0155416i
$996$	−10.2348	−	26.7266i	−0.324302	−	0.846863i
$997$	−6.54173	−	10.1791i	−0.207179	−	0.322376i	0.722078	−	0.691812i	$-0.243187\pi$
$997$	−6.54173	−	10.1791i	−0.207179	−	0.322376i	−0.929256	+	0.369436i	$0.879551\pi$
$998$	−20.9234	−	0.655973i	−0.662319	−	0.0207645i
$999$	−2.05543	+	0.603530i	−0.0650310	+	0.0190948i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.bb.a.13.20	yes	480
8.5	even	2	inner	552.2.bb.a.13.7	✓	480
23.16	even	11	inner	552.2.bb.a.85.7	yes	480
184.85	even	22	inner	552.2.bb.a.85.20	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.bb.a.13.7	✓	480	8.5	even	2	inner
552.2.bb.a.13.20	yes	480	1.1	even	1	trivial
552.2.bb.a.85.7	yes	480	23.16	even	11	inner
552.2.bb.a.85.20	yes	480	184.85	even	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.bb (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.355714 - 1.36875i) q^{2} +(0.540641 - 0.841254i) q^{3} +(-1.74694 + 0.973765i) q^{4} +(0.190010 + 0.0867748i) q^{5} +(-1.34378 - 0.440755i) q^{6} +(2.41838 + 0.710100i) q^{7} +(1.95425 + 2.04473i) q^{8} +(-0.415415 - 0.909632i) q^{9} +O(q^{10})\)	\(q+(-0.355714 - 1.36875i) q^{2} +(0.540641 - 0.841254i) q^{3} +(-1.74694 + 0.973765i) q^{4} +(0.190010 + 0.0867748i) q^{5} +(-1.34378 - 0.440755i) q^{6} +(2.41838 + 0.710100i) q^{7} +(1.95425 + 2.04473i) q^{8} +(-0.415415 - 0.909632i) q^{9} +(0.0511834 - 0.290943i) q^{10} +(4.36540 + 3.78264i) q^{11} +(-0.125281 + 1.99607i) q^{12} +(1.69874 + 5.78537i) q^{13} +(0.111696 - 3.56274i) q^{14} +(0.175727 - 0.112933i) q^{15} +(2.10356 - 3.40221i) q^{16} +(0.569168 + 3.95865i) q^{17} +(-1.09729 + 0.892167i) q^{18} +(-6.83272 - 0.982398i) q^{19} +(-0.416434 + 0.0334354i) q^{20} +(1.90485 - 1.65056i) q^{21} +(3.62464 - 7.32066i) q^{22} +(3.93147 - 2.74655i) q^{23} +(2.77668 - 0.538552i) q^{24} +(-3.24573 - 3.74577i) q^{25} +(7.31444 - 4.38308i) q^{26} +(-0.989821 - 0.142315i) q^{27} +(-4.91622 + 1.11443i) q^{28} +(0.673989 - 0.0969050i) q^{29} +(-0.217085 - 0.200354i) q^{30} +(0.246501 - 0.158417i) q^{31} +(-5.40503 - 1.66903i) q^{32} +(5.54227 - 1.62736i) q^{33} +(5.21593 - 2.18719i) q^{34} +(0.397898 + 0.344780i) q^{35} +(1.61147 + 1.18455i) q^{36} +(1.94862 - 0.889905i) q^{37} +(1.08584 + 9.70172i) q^{38} +(5.78537 + 1.69874i) q^{39} +(0.193896 + 0.558099i) q^{40} +(4.71909 - 10.3334i) q^{41} +(-2.93678 - 2.02013i) q^{42} +(-3.10617 + 4.83330i) q^{43} +(-11.3095 - 2.35715i) q^{44} -0.208887i q^{45} +(-5.15781 - 4.40420i) q^{46} +3.14610 q^{47} +(-1.72485 - 3.60900i) q^{48} +(-0.544467 - 0.349908i) q^{49} +(-3.97246 + 5.77501i) q^{50} +(3.63794 + 1.66139i) q^{51} +(-8.60117 - 8.45250i) q^{52} +(0.724646 - 2.46792i) q^{53} +(0.157300 + 1.40544i) q^{54} +(0.501233 + 1.09755i) q^{55} +(3.27414 + 6.33264i) q^{56} +(-4.52050 + 5.21693i) q^{57} +(-0.372386 - 0.888050i) q^{58} +(2.17725 + 7.41504i) q^{59} +(-0.197013 + 0.368403i) q^{60} +(-6.75974 - 10.5184i) q^{61} +(-0.304516 - 0.281046i) q^{62} +(-0.358701 - 2.49482i) q^{63} +(-0.361841 + 7.99181i) q^{64} +(-0.179247 + 1.24669i) q^{65} +(-4.19890 - 7.00709i) q^{66} +(-2.83098 + 2.45306i) q^{67} +(-4.84909 - 6.36127i) q^{68} +(-0.185034 - 4.79226i) q^{69} +(0.330379 - 0.667264i) q^{70} +(7.73672 + 8.92865i) q^{71} +(1.04813 - 2.62706i) q^{72} +(1.62593 - 11.3086i) q^{73} +(-1.91121 - 2.35062i) q^{74} +(-4.90592 + 0.705364i) q^{75} +(12.8930 - 4.93728i) q^{76} +(7.87113 + 12.2477i) q^{77} +(0.267205 - 8.52297i) q^{78} +(-2.27930 + 0.669262i) q^{79} +(0.694924 - 0.463918i) q^{80} +(-0.654861 + 0.755750i) q^{81} +(-15.8224 - 2.78351i) q^{82} +(-13.0165 + 5.94443i) q^{83} +(-1.72039 + 4.73829i) q^{84} +(-0.235363 + 0.801573i) q^{85} +(7.72047 + 2.53229i) q^{86} +(0.282864 - 0.619387i) q^{87} +(0.796589 + 16.3183i) q^{88} +(-14.0921 - 9.05642i) q^{89} +(-0.285913 + 0.0743040i) q^{90} +15.1975i q^{91} +(-4.19353 + 8.62637i) q^{92} -0.293016i q^{93} +(-1.11911 - 4.30621i) q^{94} +(-1.21304 - 0.779574i) q^{95} +(-4.32626 + 3.64465i) q^{96} +(-2.56200 + 5.60999i) q^{97} +(-0.285260 + 0.869704i) q^{98} +(1.62736 - 5.54227i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9}+O(q^{10}) \) 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9	\( 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32} + 6 q^{34} - 22 q^{36} + 90 q^{38} - 74 q^{40} + 90 q^{42} - 130 q^{44} + 96 q^{46} - 88 q^{48} - 48 q^{49} + 142 q^{50} - 142 q^{52} + 18 q^{54} - 82 q^{56} + 22 q^{58} + 2 q^{60} - 40 q^{62} - 8 q^{63} + 16 q^{66} - 44 q^{68} + 16 q^{71} - 4 q^{72} + 10 q^{74} - 138 q^{76} - 40 q^{79} - 170 q^{80} - 48 q^{81} - 124 q^{82} - 8 q^{84} - 216 q^{86} - 108 q^{88} + 4 q^{90} - 198 q^{92} - 238 q^{94} + 80 q^{95} + 4 q^{96} - 132 q^{98}+O(q^{100}) \) 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9 - 4 * q^10 - 4 * q^14 - 8 * q^15 - 8 * q^16 - 4 * q^18 + 20 * q^20 + 20 * q^22 - 8 * q^23 - 4 * q^24 + 48 * q^25 + 16 * q^30 + 16 * q^31 + 4 * q^32 + 6 * q^34 - 22 * q^36 + 90 * q^38 - 74 * q^40 + 90 * q^42 - 130 * q^44 + 96 * q^46 - 88 * q^48 - 48 * q^49 + 142 * q^50 - 142 * q^52 + 18 * q^54 - 82 * q^56 + 22 * q^58 + 2 * q^60 - 40 * q^62 - 8 * q^63 + 16 * q^66 - 44 * q^68 + 16 * q^71 - 4 * q^72 + 10 * q^74 - 138 * q^76 - 40 * q^79 - 170 * q^80 - 48 * q^81 - 124 * q^82 - 8 * q^84 - 216 * q^86 - 108 * q^88 + 4 * q^90 - 198 * q^92 - 238 * q^94 + 80 * q^95 + 4 * q^96 - 132 * q^98

Introduction

L-functions

Modular forms

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